This sounds like a problem you could have in cubase and it was fixed by finding the check box in midi setting called USE SYSTEM TIMESTAMP.
Is there something like that in x1?
You can play the drum and hear it properly in real time right?
If so then it isn't latency problem, just the way the notes are written in midi.
The workaround was to select everything you recorded and drag it to where it belongs.
You would have to turn off the snap first to do that.