I am fairly certain the credit cards are hit before the results are posted. If there are insufficient funds or invalid credit card with one applicant, another applicant can get the tag I believe.
As DRH mentioned, I went on line for my credit card and set it up so it texts me with any transaction over $20 on my credit card. Just as an example of how fast this is, when I go to the diesel pump, I usually have a text on my phone before I get out of the driveway. It's also great to have for fraud alert.