Years ago, a group of cave instructors formed an association called APSA -- I can't remember what the acronym stands for, but they came up with a set of rules for the cavern tours, and they even developed a class for the guides to take, to make sure they were properly qualified to lead. Unfortunately, it was all voluntary, and the class died, and I think the association has as well. But the rules still exist, and a good dive operator will follow them: The guide must be at least DM and Full Cave, and dive in cave gear. No more than 4 divers to a guide, and all must have lights. A pre-dive briefing must include some information about the geology, about proper diving technique in the caves, and clearly discuss gas limits. The dive must remain on the gold line, and thirds must be respected.
If those rules are followed, the tours are very safe. Where people have gotten into trouble is where the rules have been broken. I always advise people to ask the dive op if they follow the APSA rules. If they don't know what that is, go elsewhere.