By the time he relieved Riker, he was well within his right to be considering other options for the sake of the mission, & pushing him into that outburst was needed sooner rather than later. He needed all the crew to be performing exactly as expected, especially the XO. Every second of that conflict made the mission more difficult to execute.
Every single thing that Jellico did was an absolute necessity of the mission, including telling Troi to get in uniform. How would it have looked to have someone not in uniform at these negotiations? So yeah, people had to do things they'd never been expected to do before, & put out more work than is healthy to do. If Picard had told everyone that they needed to work themselves to exhaustion for the next 2 or 3 days, they'd do it without question, but Picard had years to build a relationship that fosters that kind of trust. Jellico needed that level of performance & loyalty, but knew he had done nothing to earn it.
By all accounts, the person with the hardest job of all is Jellico. He would have to have known that going in. I maintain that we never truly know what Jellico's traditional "Command Style" is. We may not even have gotten a true representation of what kind of person he is. He was playing the captain part he was required to play from the minute he beamed aboard. This captaincy, at this time, on this ship, for this mission, required him to do things that even he may never have had to do before, in a way that was absolutely necessary, & perhaps not entirely how he'd prefer to do it.
Certainly, a man who keeps his kid's artwork in his office is not a completely unreasonable hardass. Much like Picard was given no choice, neither was Jellico. He knew he'd be taking over a ship that was not outfitted properly for the task, a crew that would have no faith in him whatsoever, and a timetable that was nearly impossible. He had to know resistance was coming. If he had time, maybe he could have cooperated with them to reduce it, but he did not.
All he had at his disposal was that he's the man in charge. He was handed the uniform of an asshole & told to wear it, and get the job done posthaste, & he did. He told them it was an honor to have served with them, & it sounded like he meant it. I even felt a bit of regret in his voice, in that he never got to be the man he'd want to be with them. A sacrifice for the mission, that might follow him if he ever has to work with any of them again.
He knows they were being asked the impossible. He was too, & all of them succeeded when the chips were down. Remember when he told Troi that he wanted Lamec to think he was an unreasonable man? He needed - e v e r y b o d y - to think he was an unreasonable man. It was the only way to get the job done, but realistically, no one could have gotten to his level of command in Starfleet without being reasonable.
But we never get to see that side of him. I bet the people on the Cairo have a completely different impression of him.