Yes, all ride stops and downtimes are reported to what we refer to as DOCC. If an attraction is 101, or temporarily unavailable, DOCC removes the wait time at the standby entrance and automatically updates the
MDE app. Each time ride motion has stopped, we need to call them and let the Cast Member know the time and the cause/reason. We have to call them once ride motion has resumed. This includes stopping the ride vehicles/moving walkway to assist a guest with a disability, but we don't have to if we only slow ride motion.
In your elephant misfire example, that would not be documented via DOCC or Engineering Services. At best, a coordinator would be alerted. The Cast Member simply didn't stop the boat's movement at the right spot in time. Luckily, the elephant uses clean water, unlike what can be found in the water at Jungle, Pirates, Splash or others that require a heavy duty wetsuit if a CM needs to enter the water.
What you experienced at TTA is something called "cars ahead." It is when a ride vehicle catches up to another. Sometimes, this can cause a backup in Space Tunnel and usually will require an evacuation. After the refurbishment, TTA has been experiencing many cases of the downramp not functioning properly and "cars ahead" is being seen much more frequently. On a positive note, the turntable faults haven't been as common. This may be the reason the Cast Member didn't care, but it shouldn't be an excuse. The safety of our guests come first and all guests need to know that they are safe in our parks. No exceptions.
Another thing to note with TTA is that if the ride stop button is pressed on a handpack (a remote that controls all ride motion and all Cast Members in a safety critical position are required to have on their person), it automatically plays the emergency spiel. This is the "May I have your attention? Please remain seated. This ride has stopped temporarily and will resume motion at any time. Please remain seated, for your own safety. Thank you." This is then followed by the verbal spiel that ride motion will resume momentarily. One minute prior to resuming ride motion, another verbal spiel is played to indicate that it will resume in a minute and vehicle bumping may occur.
Please, don't be afraid. There is nothing to be nervous about. Unless you're misbehaving and not following rules, you will most likely not get injured. The rides here are very safe, even with some having breakdowns (Space Mountain) multiple times a day. Most ride stops are either to assist a guest with a disability, the extremely common guest behaving inappropriately, Cast Members unfortunately being careless when operating an attraction or just general maintenance failures. You'd be surprised which one is the second most common in that list.