The computer systems used by Immigration here in the the DR are slowly being upgraded. The data and the capabilities of the system will change over time.
It has been debated on this site for years, what exactly is the Govt's intent with the overstay fees/fines and the lack of a tourist visa for a period longer than 30 days. A respected lawyer last year posted in the legal forum that any tourist in the country longer than 30 days was here contrary to the current immigration laws and the Govt. charging a set fee to overstay the 30 day limit has no legal foundation and conveys no legal status on any visitor.
You seem to have experienced one of those annoyances that can occur from time to time when someone engages in an activity that is not in accordance with the legal framework. The DR Govt is notorious for stuff like this - the law says one thing, the Govt through indifference or inaction seems to suggest that doing something else is ok too.
The immigration system is in slow change mode and has been for the last three years at least. Will the 30 day tourist stay limit change, it may well change next week, next month or not in our lifetimes. On the day you arrived and as far as I know, for today as well, the maximum sanctioned visit for a foreigner without a formal visa is 30 days. Will plane loads of people intending to stay longer than that arrive at an airport today, certainly they will. Will they all be asked how long they will be staying, probably not. Will anyone else be detained for 2 hours, maybe, maybe not. Will you be detained for two hours next time you choose to visit this country for a period longer than 30 days, maybe, maybe not.
I personally believe that someday, there will be a change that will rework the current ambiguous immigration practices in such a way that there will be no more ambiguity. I just don't know when that will happen. Until then, it is best to, at least in your own mind, consider a stay in the DR of longer than 30 days to be a "grey legal area" that could make your legal status here ambiguous, that may or may not cause you inconvenience and/or extra expense; Or it may not.
Welcome to the often chaotic and inconsistent Dominican Republic as it exists today.
In summary, no one knows for sure what could happen if an overstaying foreigner meets up with an official that is in a foul mood on any given day. When you play roulette, you have to accept that sometimes the number comes up red and sometimes it comes up black.
In addition to the myriad of advice your story will illicit on this site, let me offer my personal opinion - Lying to immigration at the border of your home country will usually get you immediately sent packing, tossed into detention, get you a date with a judge, or banned from trying to reenter that country for a period of time. Lying to immigration here in the DR can, could, might result in the same sort of penalties. Admittedly, DR Immigration has not been too keen to look too closely at arriving visitors in the past, but there is nothing preventing them from starting to. Knowingly giving false information/answers to questions from officials (lying) is evidence of a guilty mind, in that you know the rules and are trying to get around them. The possible ramifications of being caught in a third world country breaking the law or deliberately attempting to deceive to achieve a more desirable result is not worth the risk - You do not want to be on that side of the law in this country I assure you.
If you can't come to the Dominican Republic for a vacation without having to lie or possibly break the law, then maybe it is time to find somewhere else to go. The DR currently holds all the legal cards - visitors without status who find themselves behind the 8 ball here (likely or not) have zero recourse and jail in this country is not at all like any resort you have ever checked into by way of happenstance. The fastest way to force the DR Govt to clarify this visitor stay period fiasco is to force the Govt to realize that it's own inaction and ambiguity is sending tourists and their money somewhere else.
Good luck.