Mid/Side processing alone shouldn't change what you see on the correlation meter, because it doesn't alter phase. Of course, any mono-compatibility problems that already exist can be
exaggerated by raising the gain on the Side component. That's probably what's happening.
Channel Tools does have a much-abused preset called "Increased Width". What this does is add a 20ms delay to the right channel, emulating the Haas Effect. It shouldn't introduce mono-compatibility problems, but if you were to reduce the delay you'd likely hear some comb filtering when you folded it to mono. There is another preset called "Kill Center" that most definitely causes problems and makes things disappear because it inverts the phase of the right channel.
Although CT is useful for special effects (some not mono-compatible), the only time you really SHOULD use it is for stereo panning. Never use the Pan slider to position a stereo track; always use Channel Tools to do that. It will
not have any negative impact on your audio unless the track has already been screwed up by some other processor.