Thanks Sebastien,
I had convinced myself the problem was something I’d done when rendering in After Effects. In fact, after importing into Vegas I had to tell that app the new import was to be used as an alpha channel.
For anyone else in a similar situation: render in AE with RGB+Alpha and then after importing into Vegas right click on the imported file > Properties > Media tab > Set Alpha Channel to Straight (unmatted).
Where it gets confusing is that .psd files imported with an alpha channel from Photoshop don’t need to be flagged in this way.
Cheers,
Marcus