When traveling between the dimension the experience is reset until you update it with more experience, when it is that state you can't use the experience.
From quickly looking into it, changing
https://github.com/skyjay1/Nomadic-Tents/blob/master-1.12.2/src/main/java/com/yurtmod/block/TileEntityTentDoor.java#L230
to
playerMP.changeDimension(dimTo, tel);

Should fix the issue but I haven't had the chance to look into it.

This bug does not appear to happen with 1.16.5 version. If it does... there's not much I can do about it 🤷‍♀️

Thank you! For some reason that method did not work properly in earlier versions of Minecraft, which is why I was using the PlayerList version. It works now and will be included in the next 1.12 update.

Using the method you recommended works, but it plays a Nether Portal travel sound that I'm not sure how to cancel. Any suggestions?

Marking as resolved but leaving open. Solution is to open the config file and enable this option:
# Use different teleportation code. Does two things:
# 1) Updates XP and 2) Plays Nether sound
B:"Safe Teleporting"=false

The command /xp add @p 0 points fixes the experience if run after exiting. Maybe you could just do whatever that command does?

This issue is still happening in the latest 1.15.2 version, not too big of a deal, but annoying specially when you live inside a tent