The first time I tried air drying, my ends did the same thing! I was so confused because, like you, I had gotten a trim nearly the week prior to that. It wasn't until I watched this girl's youtube video about how she got her hair to air dry straight that fixed the problem for me.
http://www.youtube.com/watch?v=P2pj4tm5GG0
She did a series of smoothing her hair down from the middle to ends with her fingertips. After I did this, my ends looked MUCH better. Also, the first time around, I didn't have any leave-ins incorporated into my regimen, but I found that when I got a really good one and combined that with Elasta QP Mango Butter (it has worked wonders for my ends, wet or dry!) EVOO to seal, and her method to air-dry, the puffiness is no longer a problem. Of course, you don't HAVE to do her way to see the results I did, but I thought if I shared that you could take a look and see for yourself. Hope this helps!