According to DOC, AMEX may report the full details of your new credit card to the three major credit bureaus around your first statement. Previously, AMEX usually didn’t report new cards until after 2-3 statements, which gave people a chance to take advantage of the timing gap. Since cards that haven’t been reported do not affect your Chase 5/24 count, this is something to keep in mind if you plan to apply for AMEX first and then Chase. In that case, you may want to apply for Chase immediately after submitting your AMEX application.
That said, based on a few data points in the comments, most people say the reporting is indeed earlier, while some say it was not. So this is still YMMV (your mileage may vary).