I was playing with my brother on a LAN world and we kept going between two islands using the minecart system connected to the world spawn. I kept seeing him momentarily appear at spawn but he said he was on an island. It happened right after he got out of a minecart on the other end so I'm assuming my Minecraft client was showing me his last known position before figuring out where he really was.

What I expected to happen was...:
My brother would exit the minecart and I'd see nothing unusual.

What actually happened was...:
My brother's character momentarily appeared at the end of the minecart track he had left from when he exited the minecart.

Steps to Reproduce:
NOTE: I do not know how this happened, and I haven't been able to reliably reproduce it. Sometimes the bug occurs, sometimes it doesn't. This is just what I'd done when the bug first happened.
1. Start a LAN world.
2. Get another player on.
3. Have the other player ride a sufficiently long minecart track (when the other player arrives at the other end, the middle part of the track shouldn't be loaded).
4. The other player exits the minecart. The clone should momentarily appear where the other player was before they entered the minecart.