Just wanted to post on a topic that I had struggled with over the last couple weeks. Initally I could only get one user to poplulate time from a labtech ticket to an autotask ticket. I was getting an error in the Integration settings that stated something like "Proxy time entry is not enabled on this system".
To reslove this error, in your Autotask Admin panel, select site setup > workflow policies. Scroll down in workflow policies until you see the Timesheets section, then in the drop down for "Proxy Time Entry", select either enable for time sheet approvers or enable for time sheet approvers and administrators. I used the second option and becuase my user within AT was an administrator, it worked.
I hope this helps.