The problem with relying in somebody else's best-case experience is that you may not be as lucky.
My first experience with Magical Express was that we were at the resort 50 minutes after we stepped off the aircraft, and we had our room key-cards 10 minutes after that. However, I would never tell anyone else to plan on being checked in at the resort 60 minutes after arriving at the airport. In fact, now that I think about it, our plane ran around a half hour late, so it really took us more like 90 minutes from our scheduled arrival time.
Realistically, it takes 50-90 minutes to get to the resort if you use the yellow Magical Express tags so that you can bypass baggage claim. At your resort, you should be able to check in, take your carry-on bags to your room, and get to your resort bus stop in 30 minutes. That would leave at least a full hour to get from POP to Chef Mickey's.
However, there are all sorts of timing issues beyond your control. Most flights arrive within 15 minutes of the scheduled arrival, but flight delays are common. DME is a shared service, so the timing of the dispatch to your resort is a matter of luck. Then, you could be the first stop, or you could stop at a couple of other resorts first. And resort check-in lines can be short or long. It's all hard to predict in advance.
So the short answer is that under normal circumstances, three hours should be enough time. But I wouldn't schedule anything with a financial penalty for no-shows.