I just checked a few of my P4s, and none of them show this behavior. After setting the display normally goes dark immediately (magnet-set version) or after 5 seconds (Auto-Set version). So, I would have to consider what your watch is doing, a new symptom of aging in Time Computer electronics.
As a side note...on the 800 module (Auto-Set module used in the Men's Sport and Touch-Command Dress), if the minutes are set, a single blinking colon dot remains on after the display blanks, presumably as a reminder that the watch was set, and needs to be re-started for normal timekeeping.