Rosecrans is criticized for not starting Tullahoma sooner
My criticism of Rosecrans is with his personality. The timing of the campaign is actually a good example of how his personality gets in his own way. He creates a problem with perception all by himself.
I have often wondered what was delaying him, but not because of anything anywhere that anyone has written about this, but because of Rosecrans himself and what he wrote, the reasons he gave, and what was on his mind.
Of course I am going to wonder what's delaying him, upon reading a dispatch where he states that he took a survey of his senior subordinates and they all agreed (except one) to wait to advance. That says nothing about what the holdup is, or when he's expecting it to be resolved. Moreover as Halleck points out, that's not a valid military reason by itself. The responsibility lies with the commander and not a committee.
Another time, Rosecrans stated that he could better hold Bragg in place by staying static than by advancing. Bragg would in fact detach forces to reinforce Johnston, but that's beside the point that he also doesn't explain why he thinks advancing is going to push the enemy towards Grant. His reasoning was off and the President knows it.
Then he wrote that it was against some military precept to fight two different decisive battles at the same time. That made no sense and instead prompted me to think that what was on his mind was the publicity for his victory in the papers when it came. He didn't want to be eclipsed, he was playing the press and public opinion there.
Overall, he created an impression of being dilatory for no honest military reason by citing all these extraneous excuses. He could have been straightforward. There were times he had crowded the telegraphs with so much detail with no urgency that he was reprimanded for doing this. Yet when the administration was pressuring him to prevent reinforcements from being sent to raise the Vicksburg siege, he was raising objections that did not make military sense.
He eventually was threatened by Halleck (who wouldn't have done this without Lincoln approval) that if he didn't advance, he was going to have part of his forces sent to reinforce Grant, and only after that does he finally move.
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In all this, Rosecrans just created a negative impression all by himself. Then, he had written to the President demanding that his commission be backdated to supersede Grant, to which Lincoln responded, in essence, you presume too much, setting him straight as to who held the power in that relationship. That's actually an incident that revealed how Rosecrans would push boundaries when it came to authority.
Then all these remarks were made in the context of Rosecrans' stubborn antagonism with Grant, which the President knew because Rosecrans wrote about this to Halleck, plus he then made all those efforts to outrank Grant explicit. Therefore one is left with a lot of questions about what was really motivating Rosecrans, and the problem is that all these questions and nebulous reasons derive just from Rosecrans own writing.
Again, he might have had a justifiable reason, several possibly. But he could have stuck to that and avoided all this extraneous stuff that just comes across as power hungry plays. And the thing is that this negative inference will always be there because it started with him, it comes across from his dispatches and letters.
As to criticisms that others may have about one thing or another, before or afterward I don't have any formed opinions, but I do know what (or rather, who) made me suspicious about the issue of his timing.