Addictive Drums 2 sounds coming in an eighth note early?

Try muting the Coolsoft tracks and record another midi track using something else (like any of the included soft synths). If the new midi track plays in sync with AD2, then it's likely the Coolsoft synth is doing something weird. Also check the event list to see which synths are having events where you expect them and which are not. I always leave two blank measures at the beginning of a song to make room for any time shifting, if necessary. At least you have a workaround until the matter gets resolved. If all of the midi events appear where they should in the piano roll and event list view, check to see which tracks don't sound where they should in relation to the "Now Time". A delayed track could be caused by monitoring the sound on that track through the software, while the undelayed track is being monitored directly. Experiment with the midi echo buttons to see if that makes a difference and check your sound card settings to look at your monitoring options. It seems unlikely that that sort of delay would be that long and sync perfectly to an eighth note, but you never know. Also make sure you don't have a delay effect set to 100% wet synced to an eighth note with the feedback set so low that there is only one audible repeat. Stranger things have happened.

I would simply check whether the audio transients of the frozen AD2 track align visually with the timeline grid and sync audibly with the playback metronome. If so, then the issue is Coolsoft latency as others have suggested.