Travelled on AA just a few weeks ago (PUJ-MIA-PUJ). I had checked online beforehand to get an idea of how busy the airport would be at 5am and planned accordingly. Got there over 2 hours ahead of departure and proceeded to wait in line at the AA counter for over an hour (they opened it 1h50m before departure). The line was long but not THAT long but it took a long time to get through. Staff were doing a lot of typing on the computers, calling the supervisor over every 5 minutes to help them with something, needlessly walking back and forth, making jokes with each other... you get the idea. Once checked-in, the rest was a breeze. No lines at the security check or migracion. By the time I got in, went to the bathroom, got something to munch on and found my gate I had about 10 minutes left before boarding started.
The return however was not fun. All the gates were full and 2 planes had just landed before us. Having my residency, I was permitted to go into the shorter line which is supposed to be for legal residents and people that have already purchased their tourist cards. If you're not provided with a tourist card by your airline company BUY IT ONLINE IF YOU CAN. The line to purchase the tourist card was ridiculous, zig-zagging back and forth and no one knew where they were going and what they were supposed to do. Half the people in my line weren't supposed to be there (tourists without tourist cards) and there was only 1 customs agent for us. The rest had 5 agents for the hundreds of people waiting. I used to think that the setup they had before was bad but this is worse (except they can fit more people under the roof now). Signage is practically non-existent, many people don't know they have to pay 10USD cash upon arrival for their card and although the staff tries, they can't keep people in line. At Miami it was almost scary to see so many well-behaved people standing in line quietly. Apparently when one leaves the "civilized" countries, all that education goes out the window... When I finally managed to get thru migracion, my suitcase was already waiting for me on the floor by the carousel. I was impressed to see that they now have staff that makes sure people are taking the correct suitcases, checking with the client's tag and the tag on the suitcase. Of course when I went to pass thru the last security check I was pulled aside to check my suitcase. Happens every single time. White woman travelling alone=drugs or good opportunity for extra cash. I went mumbling and grumbling in spanish towards the line with my overweight suitcase when the same guy that had sent me there comes back to me and asks me if I was from Higuey. I told him no, I lived 15 minutes away. He winked at me and told me I could leave. That was a first! lol
So lesson learned, plan to be at PUJ nice and early if you don't want to wait hours in line and if you don't have your residency or your tourist card included in your flight, buy it online.