It's, from what little I know of it, is a far cry from any submarine that immediately comes to mind. It's a very specialized tool, not a tool of war. This vessel goes down and up. I'm not even sure it has much ability to move other than ascent/descent. Very simple and, from it's record, extremely well constructed and properly equipped. Numerous successful trips up and down would certainly indicate such. Ballast control is fairly simple I would suppose, water in, water out. Even an "emergency" ascent from great depth would be slow and carefully controlled. Unless someone here has intimate knowledge of the craft, we are all pissing in the wind with our observations/supposition(s) as to construction and operation. Well, other than the basic application of some even more basic science with regard to pressure and effects on alien intruders into the great depths.
Such travel, like most anything, is usually very safe until ... something major or minor, goes horribly wrong. Really no different than people paying for a frivolous ride into space. Weigh the risks, access the reward then make a decision. If you really want the experience, you must take the risk.
I would have loved being able to speak with the "tourists" before the dive to learn what drove them to do it. Was it just a "jaunt"? Was there something about themselves they wished to learn? Did they have a serious "hobbyists" interest in the Titanic? Perhaps they will survive and I'll learn the answer. Just curious as to the thought process.