Wow, that really sucks! All of my tanks are on the first floor which is ceramic tile over terrazzo. I've considered maybe putting one upstairs eventually which is tile over backerboard over plywood. Should be ok but I think I will seal the grout extra well.
kamoton; You mean the bottom of your stand has an area you can't get to? Use a hole saw to gain access. Or you can use a jigsaw and saw a large access. Then you put a few little tabs on the underside and the cut out section can drop right back into the hole flush. I've done that under a few sinks for various reasons. Work pretty well.
I would watch your floor for a week. I suspect that if it doesn't go psycho on you by then it isn't going to. Often if they react badly it will be really evident. Like so bad, it looks like large foot long potato chips laid next to each other.