Hey there @fatlob!
I know that problem, but I haven't seen it around in quite a while. The character can freak out like this sometimes if you're trying to fly upwards by more than the suit can feasibly carry you, but that doesn't seem to be the cause in this case.
If you don't give any input at all right from the moment you spawn, does it still do this? How about with your mouse disconnected momentarily? Also, how's your framerate? We might still have some physics incorrectness on low framerates, but on the other hand it seems fine in your youtube video. How's your mouse sensitivity set?
Do you have any gamepads, joysticks or other gaming controllers hooked up that you're not using?
Could you send me the game's log file after running it? It's found here:
Win: your-steam-install-dir\Steam\steamapps\common\Volo Airsport\volo_airsport_Data_\output_log.txt
Linux: ~/.config/unity3d/Ramjet Anvil/Volo Airsport/Player.log
Also, thanks for jumping in and helping out @Jens_Hagen, much appreciated.