Human beings are hard-wired to quickly and instinctively read the emotions written on the faces and expressions of other human beings. I doubt it took more than a second for her to decide "that man" (hereafter, TM) was "panicky", if even that long. And she didn't associate the man with the notion of "running from the police" until at least after Johnny Brewer went in to see if he could find him.
Think this through a minute, Mitch. She sees a panicky looking guy coming toward her and her first instinct is to turn her back on him and look the other way?
Brewer didn't start in the direction of the Texas Theatre until after he saw TM disappear into the theater entrance 240 feet away from where Brewer was standing, so "immediately" may not be the best word to describe the period between TM walk into the theater's entrance recess until Brewer got Postal's attention.
Perhaps not, but how long do you really think Postal stood there staring west?