The only person being unprofessional was Mourinho. The 'troubled' Pogba turned up for training along with everyone else, smile on his face, ready to train and Mourinho decides to say something and start a fight which puts the entire squad in a bad mood for training.
Fans generally have dumb ideas about what makes up a professional player, he's posting on instagram, clearly he's not putting in 100% in training or trying hard in games, bull. When a manager screams at you for making forward passes that don't come off you stop making forward passes the same way if your boss screams at you for taking initiative you stop doing so. Mourinho's Utd, Chelsea, Real Madrid, Chelsea again, when they fell apart it was offences that looked entirely afraid to be at all creative, who were being told don't make the runs, don't commit to support counters in numbers, stay back and don't misplace passes.
When the big name player seems to not be helping with goals after costing 90mil, fans get stupid about it, in reality he was being hampered by being told not to be creative, not to attack, not to burst forwards and the same went for many other players. Martial was just as 'bad', as was Rashford, and Lukaku. When given freedom and told hey, I want you to attack, I want you to express yourself, I want you to play as you play best then the entire offence started playing better. Now it might be 3 players flooding in to support a counter rather than 1 player and it opens up more options. Now Pogba doesn't wonder if he'll get shouted at every time he tries to pick out a throughball so he does it more, because more passes are going forward the players are making more runs, etc, etc.
The only person I ever saw acting unprofessionally was Mourinho, video's from training, his interviews where he crapped on players and absolved himself of all blame by stating he had league titles, etc.