I had this happen on a couple Public Servers. I was on the Aerobatics, and I would see all my friends actions on his aircraft, like closing his canopy, throttling up, rearming, but his plane did not move from that position. We then went to a training server, dont remember the name, and this happened again, he would not move, although he was moving on his screen.
I also had this later on in the day while playing by myself, I asked a question in the server chat and I told them my position flying over an airfield miles from where Ive taken off. But when they tried looking for me they only found me at the airfield I spawned at on the ground.
I switched back to stable with my friend, and we never had the problem again. Super weird.
Edit: These were all in official DCS planes