I find the ability for any character to jump behind their current melee target and get an advantage from it quite ridiculous. It makes min maxing tactical combat a monkey jump fest. Once you are in melee, you shouldn't be able to jump behind adversaries who are already in contact with you. This is stupid and has to go.
It clearly puts me out of the combat immersion, because it's so exploitable to the point of being utterly broken in my opinion.
If it's immersion breaking like you say, then don't use it.
In the scenario you described, current melee target, there is no reason for you to use jump/disengage if it breaks your immersion. Just use your move action to move behind your target, making sure not to leave their threat range.
Per the 5e rules the DM is free to award advantage for any situation that they deem appropriate. Our DM, Larian, gives advantage for being behind a target(and attacking from high ground).
In the situation you described you currently have a way to get behind the target without breaking your immersion.
