I'm no expert, but when I have boated in the tropics in coral areas (which are generally nice places to boat, especially if you like to dive and snorkel), we took a lot of care to not anchor in coral. At that point (twenty years ago) we were not thinking of fines, but of damaging the coral we loved.
Fortunately, at least in our size boat (not a superyacht), coral area anchoring is usually reasonably shallow, and also the water is clear. General rule of thumb was to only move the boat in the morning or mid-day because in the afternoon it can be very hard to see into the water due to glare (so you can run aground in addition to it being harder to see where you are anchoring).
Some areas are big and sandy, so it's fairly obvious. In other places we had someone on the bow calling out where would be a good spot to drop the hook (once we had already identified a general area). If things didn't look good vis-a-vis coral after settling, we'd move and get a better spot. Not only would it damage coral to have your anchor or chain running over it, but I think it could be noisy and unpleasant.
We also usually took a swim to check out the set, but then we were there to swim and enjoy the water anyway. We learned quite a bit about our anchor and setting technique, because in our home waters these things were not possible to see in real time.
Another factor that may work in your favor (but is I'm sure location and season dependent) is that there may be consistent trade winds where you are in the tropics. That can make the boat's motion while you are anchored more predictable.
Long story short, move boat in later morning or mid-day but not later (so you can see into the water), choose a sandy spot, and keep an eye on things (coral water has always been clear water when I have encountered it, although obviously I have not boated everywhere).
I think modern anchors could make this process easier. With our old CQR (which was modern back then
) it sometimes took a bit of distance to set, making prediction a bit more of an art.