Definitely not a timing bug, although it may be a mission bug... I just confirmed that the transport does just head off towards its starting position in the original game too (GOG release). It played out the same way in WCAT. If you land once the transport starts flying back then that completes the mission successfully. I believe it's supposed to enter formation with the Tiger's Claw, but that isn't happening.
The ace wing however did spawn correctly in both sessions, so I'm honestly not sure what that could have been, unless you manually flew around the area where they spawn on the way to the Tiger's Claw? Not sure!
I'll have a look at the mission data and see if I can stop the transport properly at the Tiger's Claw. I'll have to test it in the process, so I'll see if I encounter the issue where the ace wing doesn't spawn.