AFAIK, there is no reason not to add it in the primary bucket. It will work just as well as it would in secondary.
As far as the Oxygen thing goes, you won't get any more exposure to oxygen by opening the bucket and then closing it than you would for opening the bucket, transferring it to a carboy and sealing that . . . even with the lower headspace in the carboy, the transfer process introduces more oxygen than simply opening a bucket lid. In fact, as you'll likely have a thick layer of CO2 on top of the bucket, you might be safe.