It turns out it's not as straightforward is one would hope:

1. If you have miles as a preference in your Choice profile, and you book through the website (using your Choice #), all is well.

2. If you book on the phone or in person, they will default to points unless you specifically request miles at checkin, and you give them your FF number and so on. You also have to make sure they do it, because a lot of the front desk folks don't know how, so they might have to call a manager.