billing information not complete when registered.

Hi,

That's not possible unless you removed the "address" view from your checkout workflow. In that case, someone only need to be logged in to finish the checkout, the address is not required. So if the user registers through the checkout, he will have to fill the address if you activate the "ask address on registration" setting, but if he registers through the joomla registration and then logs in, he won't have to fill his address during the checkout.
So you should make sure that the "address" view is in your checkout workflow.