I did what you asked me and my EntityItem is now in my TE, but that didn't fix my problem. Also, you told me to set the position only once but I can't, that's the reason the item was following me. I found out that the xyz of renderTileEntityAt are dynamic and depends on the position of the player. The animation is not working and I honestly don't know what to do now.
TESR:
Tile Entity:
EDIT: Thanks to everyone, I finally found out why the item wasn't moving: the render uses the age of the item to animate it but the age of my item wasn't updating so I just created a int and I add 1 every tick.