in the terminal issue the following command
sudo tmutil disablelocal
That will disable local TimeMachine snapshots.
I don't know if it disables the autosave feature as I generally don't use any apps that use that feature. Given that this local TM snapshot is only enabled for MBPs and not desktops, I'd say no.
This is not turning Time Machine off either, just local snapshots, TM will continue to back up as it normally would but it will write the back ups to the back up volume
My next question would be, what is the difference between local snapshots and TimeMachine backups? (This is my first Mac since OS 7)
I can confirm that with TM disabled, autosave and versions work without any issues (though for me I wish it turned them off)