It is unclear if that was presented as part of Davis's fondness for sharing what he thought with Lincoln or if that was ruled from the bench, but assuming the source can be trusted (I don't have any reason to doubt it, but I don't know it - which says absolutely nothing, I'm just observing in case someone who has read it can come to either its defense or note its unreliability), that does, indeed, make it clear Lincoln had at least one respectable judge say there was something wrong with them.
However, it is unclear if he was condemning their use - but not Lincoln - or both.
Lincoln did not, unless my memory is sorely failing me, order military tribunals - so for Davis to declare them unconstitutional and wrong does not mean Lincoln violated the Constitution over them.
After all, while it can and probably should be said Lincoln should have done something about the subordinates who used them despite his preferences, the violation of the Constitution was done by them.
As for the issue of Coles County, sadly your link does not tell us anything (or at least I didn't see anything) indicating Davis telling Lincoln that the Constitution is being broken by his behavior.
Good link though, thank you for adding it to the list of known resources.
Cole County was in Illinois, a western state. So Davis was referring to Indiana and Illinois. There were other trials in these areas that didn't get the publicity of Milligan's group and the Charleston Riot. Had not Milligan been a lawyer, he would probably been hanged and forgotten.
I'm not a Lincoln basher or lover. The heavy hand he put on the northern people bothers me as much or more than his total war policy on the south.
Thanks to ex parte Milligan, that kind of executive power didn't surface again until WWII and post 9/11. That kind of executive power, each time it is applied, leaves some still intact even after peace. You could call it a slow snow ball effect.