I was going to suggest that you need to select Export Animation before exporting:
However, when testing this with Heidi, which has a Perform menu, it didn't work.
I imported Heidi in 3DXchange, which shows all actions in the Perform Editor, and then exported.
The re-imported Heidi has no Perform menu in iClone. I also tried with Export Animation checked, but that didn't make any difference.
So you may have discovered a bug...