You have likely came across an instance of Minecraft bug MC-98153 related to anti-cheat functionality, still existing as of 16w44a.
The issue is that due to the new teleport acknowledgement system, after moving through the portal, the server sets the player back to the last position acknowledged until the client acknowledges the new position later causing a rubber band / teleport.
Workaround:
Remove all fire/lava at the exact location of the entry portal in the other dimension. E.g., if you have a portal at (100, 64, 100) in the overworld and you are set on fire when going to the nether, go to (100, 64, 100) in the nether (not to the location of the exit portal) and remove fire and lava around that location.
I have just encountered the same issue in 16w44a and I’m not looking forward to that Nether hike