He's their manager, if there's one thing he's great at it's motivating his players, whether it's before games or after defeats. Could there have been words? Yeah of course but I don't think that's unusual in such a highly competitive environment.
Did he abandon the team and didn't travel back with the team? I would highly doubt that and nothing suggest that this happened, given that 95% of such rumours on Twitter are bollocks.
If it really happened like that it'd be very strange and childish indeed yes