This is an amazing coincidence… I just posted this exact same problem/question to the Avid message board just last night. The only difference is that I am using DV footage instead of HD. The exact same problem happens when I export quicktime-animation codec from AE and import in Avid.
Indeed, even the 2 files (original and AE-modified), as viewed in the AE timeline, are perfectly matched up… so this leads me to believe it is directly related to something in the Avid import process doubling frames.
The following is a link to my post in the Avid forums
https://www.avid.com/exchange/forums/30345/ShowPost.aspx
I have found that if I use the dvcpro codec (not the AvidDV codec) it seems to work although Avid warns that I am using a different resolution than my project. I would like to output a higher resolution file from AE though, such as Animation or None.