Having been trained to listen to the hum of the magnetron for several reasons (among them: it affects how popcorn pops and if you are in lunch room setting with a complete mixture of models you have to listen to know which sort of microwave you "lucked" into that day and adapt to its challenges to avoid burning popcorn) it takes a surprising amount of time for even a good one to spin up to full speed as much as a quarter second. As microwaves age or get cheaper some of them take a full wall clock second or two. Some of the cheap models even lie to you and don't start their own timers until after the magnetron hits full speed.

Something that becomes more apparent the more you listen (but also if you actually pay attention to diagrams of how a microwave works): the magnetron is a spinning thing with its inertia. Even if you immediately cut power to it, it still spins on its own for some amount of time. Given how much energy and wall clock time it takes to spin up to full speed, it shouldn't be surprised it needs similar wall clock time, if not energy to full stop.

But also, yeah the door pull sensor is a classic analog latch detector that has a slower sensing time than a button would by its very nature (and trying to avoid false positives from a loose/vibrating door). It's an easy thing to cut corners on and some sensors are worse than others.

(And also, safety certifications include a margin of error that it still "generally regarded as safe", what's a few extra microwaves escaping into your body among friends as long as it isn't full power?)

If I'm understanding the paper correctly, the bursts had a mean duration of 0.14 seconds, which for a 1000 W microwave would expose you to 140 joules, enough to heat about a shot's worth of water by 1°C. Seems plenty fast to me.