The idea is a pop up on a card will lock you out of that card and the same family of cards (at least temporarily). For example, if you apply for a Hilton Biz and get the pop up, you’re locked out of the Hilton family of cards, i.e., you’ll get the pop up if you try to apply for the Surpass, Aspire, or Hilton Honors card. At least, until one of whatever criteria Amex uses to weigh your “history” (e.g., spend, age of cards, opening/closing cards) changes.
If you get a pop up, the theory is to immediately apply for a card in another family of cards, like a Marriott Bonvoy, Delta, or Amex-branded card, and the pop up shouldn’t carry over to the different family. If you wait to apply, say until the next day, Amex will probably re-run the pop up algorithm and the pop up might reappear, even on a card from a different family, if nothing material has changed in your “history.”