On version 5.81 on MC 1.11.2 with forge version 13.20.0.2222 (just the versions I confirmed with. This was first noticed on 1.10.2 with RF Tools version 5.59 and forge version 12.18.2.2124) the player view while riding a horse up an elevator teleports the player around and on high enough distanced (~20 blocks ) the player and horse will drop out of the elevator and teleport to the original location while the elevator will continue to its destination.

Thank you for taking the time to create this issue, as we're no longer supporting versions below 1.12, I'm going to go ahead and close it but if this bug seems to continue over to newer versions, please do report it again so we can investigate the issue further.