I've used it for years with no problem.. I quantize the chord track so all notes of a chord start on the beat, and at the same time.. Variations in the start time of individual notes of the chord track, could lead to the problems you describe..
Also look at Logic sync page, and see what the MIDI play buffer is.. It defaults to play a bit before audio tracks, but that should not be the issue.. If that got knocked way out, could be an issue..
You also want to quantize the lengths of chords, so all notes end at the same time. If a note ends short, Real Guitar will think it is a different chord.