Join server with correct skin and username, but wrong inventory, experience level, and position

Scenerio
3 players were playing on a server that was hosted from a laptop in a single player game that was opened to LAN. I was playing on another computer, not the Laptop. Later I tried to start that same single player world on the laptop, but join with my username that I had previously used on the other computer.

What I expected to happen was...:
I expected to join as my character that I originally played as on my desktop.

What actually happened was...:
I actually joined with skin and username of my character, but with the inventory, experience level, and location of the player who originally hosted and played the server on the laptop.

Also just to see what happened, I logged in with the other player's username, opened the server to Lan, then started a 2nd minecraft client on the laptop and joined the server with my username. We had different skins, but the inventory and experience was the same for both characters, and we spawned in the same location (the last position of the other player).

Steps to Reproduce:
1. Laptop with username 1 start world in Single Player, and open to lan
2. Usernames 2 and 3 join server from 2 different computers.
3. After playing (Tried a few days later)
4. Username 2 tries to start the same world on the Laptop, joins as username 2, but has the inventory, experience level, and position of username 1.