As others have said, on my first visit, I believed they were really moving. I was 9 years old, and it was 1986. (Living Seas was brand new, only open 3 months!),
But by the time I made my second visit at age 18, I wasn't fooled (and probably already had read somewhere that they didn't move). But then again, I've always been involved with theater and know a bit about visual trickery and illusions...
In fact, the floors *did* move about an inch, to help give the illusion of the hydrolator starting and stopping motion. The shaking floor was a little more obvious on the exit/ascent hydrolators because they typically weren't totally full, and you could see the floor moving where it met the stationary walls.
And the person who supposed that Otis is a subsidiary of the original sponsor United Technologies, you'd be right. Otis did actually supply the door mechanisms, so they looked like real two-part elevator doors that everyone is used to, adding to the illusion that you were entering a real elevator.
The exit hydrolators didn't have windows because even though they could do ascending rocks quite easily, the bubbles in the water outside the windows wouldn't look right. So the windows were just blank panels, and the roof had some kind of frosted skylight in it with a lighting effect above. (It may have even been a moving light that got closer to the car as you neared the "surface", I don't recall)
Martin's Living Seas Tribute video has video of the Hydrolators.
http://www.martinsvids.net/?p=61
It's a great video, I suggest you watch the whole thing. But if you want the Hydrolators right away, fast-forward to the 15-minute mark. You even get to see some of the outside effects that people missed if they got right on a waiting hydrolator, like the descending/ascending lights on either side of the doors, the bubbling of the water under the bridge to the doorway and the sound of the Hydrolator car "arriving".
The exit hydrolators are are the 30:40 mark in the video.
On a side note, the now-closed Star Trek experience in Las Vegas handled their turbolifts slightly different, though I'm not sure it was more-convincing... They used a single car that only had one door. You entered from one room (the bridge) and as you were supposedly moving down through the ship, the car slowly rotated so that it faced a different direction when the doors opened and you exited out into a totally different set than you entered.
-Rob