Hi Ash, thanks for your post. Which tempo algorithm are you using? Pitch or time stretch? Also are you using Ableton Link?
It would be very useful if you could send over your GTL session so I can open it up and see what's going on.
You can use iTunes file sharing to drag your session folder over to your desktop. If possible, zip it up and send it to info@grouptheloop.com using WeTransfer.
Cheers!