If you stare down a hallway for more than 3 rounds with Detect Magic on, you can get full information about everything in that hallway. But do you also get full information about someone who just entered the hallway on round 4? Or do you have to wait until they've been in your field of view for 3 rounds to get their aura strength?
From the Detect Magic spell description, Core Rulebook, p. 267:
The amount of information revealed depends on how long you study a particular area or subject. (emphasis mine)
Thus, information which is principly about the area would be available once that area has reached the target number of rounds, while information principly about a particular subject, such as the new arrival in your example, would not become available until that subject has been in the area of effect for the target number of rounds. This is a very subjective judgement, and the RAW has no further help to offer with this.