Thank you, milandro.
I heard back from Gabe at B&H last night. Here is his email to me. [emphasis mine]
"I actually never noticed it until you sent me the email and I just tested mine and it actually does the same thing. I asked my friend at Fuji the details and he replied:
The movement is the lens quad linear motor focusing mechanism when not engaged. We need more education on that. They are disengaged when power off. So they rock a bit then when AF [is] on they roll!! Fast n quiet AF.
Hope that helps and enjoy the new lens!
Gabe"