Well, it ain't easy--and nothing is permanent, but you can fix this problem.
Prepare to work hard, in the sun. Or in the alternative you can locate, pay well, and supervise closely a couple of diligent workers. It's a seriously daunting and depressing job to tackle solo, although it's possible to do so.
First, disconnect your cistern. You don't want all of the crud and debris that you are going to generate to flow into your water system.
1. The problem recurs because water has found it's way under some (many) apparently sound areas previously coated with one or another of the latest whiz-bang elastomeric, siliconized, rubberized, fluid-applied membranes. Applying a "fresh" coat is both easy and temporary. Pretty easy, and very temporary.
This water, trapped in between and underneath the layers of your roof coating wants out. And water WILL have it's way, either steaming it's way to the surface and violating the integrity of the latest whiz-bang coating in the process, or rotting the concrete and rusting the re-bar on its way to the inside of your home. The only way to treat this is by removing ALL of the unsound coating. Heed my words, or at least recall them a couple of years from now it you yield to the temptation to take short-cuts in the preparation work
2. Buy yourself a couple of 4" wall scrapers with replaceable blades. In fact get three. That way when one breaks you and your lovely assistant can continue scraping, scraping, scraping as you peel away layers and layers of failed coatings. Wear gloves to protect your knuckles. Avoid using a grinder or a power wire brush--that will only polish the cement and make adhesion of new materials problematic.
3. Chip away and scrape failed concrete to a relatively sound substrate. If doing so exposes rusted reinforcing rod, clean and prepare that metal. There are a couple of products, now more or less readily available in the Dominican that will chemically alter the rust, magically consolidating it into solid protective coating that you can then paint. I've no idea how this works, but it does.
So: clean the exposed metal, apply miracle conversion product and then prime. Once the primer paint is dry thoroughly wash any cavity or depression in the roof surface created by your work to remove all crumbly concrete and dust. Apply diluted concrete bonding agent with a small paintbrush as directed and while the bonding agent is still wet place a 1:1 sand and cement mortar fortified with additional bonding agent.
Cover any of those patched with a damp rag to retard evaporation and allow the chemical process of cement curing to proceed. (Full cure requires 28 days, by the way, and no cement should be painted or coated before fully cured. I'm just sayin'.)
4. Reapply your serious sunscreen and fight over who gets to wear the big floppy hat, wear the knee pads, and use the kneeling pad.
5. Scrape, scrape and scrape from all different angles.
6. Be amazed at the amount of mold and algae hidden within and under layers of roofing membrane. Good riddance.
7. Sweep well and then scrub the roof with detergent--and don't skimp on the bleach.
8. Finally, pressure-wash the entire roof. Scrape the newly loosened edges of the remaining existing coating. Wash with bleach and water a second time and then rinse well.
You now have 2 or 3 grueling days or more invested in this project. This level of detail in preparation is important to a successful job. Without it you are just pushing your problem down the temporal road, so to speak.
Avoid heatstroke (Seriously). Work early in the morning and again in the evening. Stop when you're tired. Tomorrow is another day, and this is not a speed competition. Be smart, be diligent. Do I need to mention the importance of staying hydrated?
Materials:
In my lifetime I have applied hundreds and hundreds and hundreds, probably many thousands of gallons of fluid-applied membranes. The gold standard is a product manufactured by Minnesota Mining and Manufacturing, 3M. It is a roof and deck coating for designed to waterproof roofs and planters in commercial buildings and the decks of parking garages. You can't buy it, because 3M only wants people who understand the importance of proper preparation to use their product. There are other solvent-based competitive products that are pretty OK in my experience, but probably aren't readily available here. If you want to go that route, find someone who is roofing and waterproofing a high-rise in Sto. Dom. and ask them where they get their material.
I am fortunate to have 5 "flat" concrete roofs here in the RD. None of them have a fluid-applied membrane coating now, nor will they in future.
Believe me when I say "been there; done that--and ain't gonna go there no more." Because there's a better way. And because you did all of this onerous labor in preparing your roof you're interested in the better way, right? But before I get there, let me offer a final suggestion to those who are determined to go the siliconized, rubberized, whiz-bang elastomeric coating route anyway: begin by applying a dilute coat over the whole surface, what we used to call a "wash coat." Then attend to detailing the cracks and any patches you've made with a brush and full-strength material, or material maybe slightly thinned with water. Work the material across the cracks and then in line with the cracks, but avoid over-working the material. Feather the edges and try and minimize bubbles by lightly "tipping" the material with your brush. It's just what it sounds like.
You're not doing this in the direct sun or in the heat of the day are you? Stop that.
When dry, I'd apply a full coat using a brush, taking care to minimize the occurrence of bubbles in the coating. And THEN a second full coat, perhaps using a roller but in any event "laying off" the coating in the direction that water will flow on your roof. Easy Peasy.
A different approach:
The Thoro company manufactures a cementacious product called Thoroseal, and the Ferreteria Americana carried the product for about 20 minutes fifteen years ago. I've looked high and low and never seen it since then, but if you find it let me know.
Since then I have found 2, maybe 3 suitable alternatives. These products are all purchased in powder form and most are mixed with a special bonding agent using a paddle mixer and a half-inch drill motor. The resulting slurry is applied with a mason's brush, first detailing the cracks and patches as outlined above, followed when dry by a full coat tipped off in the direction of water flow, as above. And then a second coat.
After a couple of years you might want to wash the roof and detain any cracks that may have materialized in the intervening years--it's just a matter of respecting and protecting all of the work you did in the first place.
The Sika corporation makes lots of pretty terrific products, including a cementicious waterproofing and bonding agent as described above. This stuff is readily available in the large newly remodeled ferreteria in Las Terrenas, among other places.
PlanaSeal 88 is another good cementicious coating, mixed with a special bonding agent and water. Available at the Ferreteria Unidos in the Capital.
Finally, Laticrete makes a "Hydro Ban Cementitious Coating" that is a powder that you mix only with water. It's available through the ceramic store on the Av. 27 de Febraro, located neat the Volvo dealer (but on the other side of the highway.) Bring the big check book. I've used this product under tiles in the walk-in showers and also to coat the inside of new cisterns. (Actually, I stopped a streaming leak in a concrete cistern 15 years ago, using hydraulic cement and then Thoroseal , applied to the OUTSIDE of a nearly full cistern. Still holding.
Anyway, for what it's worth: there you have it.
Take your time, you'll be glad that you did later on this year when the rains come and you're recuperated and are ready to tackle repair of the interior water damage, now that it's dry inside.
Best of luck.