In order for a clip to sync to tempo on the timeline the two following things must be true...
1. The track you drop it on has to be set to Timestretch in the Inspector... and ...
2. The clip or loop has to have a tempo reference (check the clip Inspector)
In your case we know it has #2 above because it conforms to tempo on preview in the browser so the issue is likely that you need to set the track you drop it on to "Timestretch" in the Inspector.