Radio signal travels at 186,282 miles per second in a vacuum, a little slower in normal atmosphere, so if they are closer to the transmitter, surely their pager will go off before your scanner. I am kidding of course.
How much time are you talking about from their jumping, to you hearing on scanner? Others will surely correct me, but I think some pagers can be activated with just the first tone to go off, could there be just a smidge of time between tones going off, and your scanner catching up with their page out channel? Was the scanner in scan mode or locked onto the channel? Physic pagers maybe?
My answer of course is more for comedic relief and not to be used as a real answer.
That is what I was getting at in my post about the 'simulcast', our FD pagers are on VHF but the dispatch is on the Trunked 800 MHz MOT system. They make the 'voice announcement' simlutaneously here in my department.