They are probably some species of amphipod.
According to that link, two species common to Florida are Talitroides topitotum and Talitroides allaudi, though there are dozens of species in the US alone. In some areas, amphipods may be known commonly as "scuds."
These guys like to live in fairly wet places, depending on species - on the beach, in decomposing mulch/leaf litter/grass. They seem to be finicky with moisture: they tend to seek drier areas when it rains, often bringing them onto sidewalks or indoors, then they get dry and look for moisture. I'm guessing this is how they end up in your cat bowl: you certainly are not the first one to observe this.
I'm not sure at all about the precise species...the species most commonly encountered by people on the sidewalks and such don't seem like they would survive long truly immersed in water since they avoid rain, but I wasn't able to find anything definitive on that - maybe their behavior is to avoid very wet but they can still survive immersed for awhile.