It may vary by CC, or by reporting service? I'm basing the "non immediate" on examing my Equifax alerts online*. The inquiries were sometimes as soon as a few days, but more often weeks, implying that they only reported a couple times a month, and it all depended on when within their reporting winodw you applied as to how quickly the inquires post.

(But it's quite possible that the reporting frequency differs by CC, by reporting service, or even for each combination of the two!)

*For a while now, Equifax has had a free alert servcie for PayPal members. Unfortunately, they just sent me an email recently saying they're discontinuing that free alert service at the end of January.