If your fan shut itself off after a few minute, it is functioning as designed. Most new cars have a thermostatically controlled electric fan, so when you pull into your garage or whereever, it stays on long enough to cool down the coolant, and thus protect the motor IF you had run it hard, AND/OR had just shut immediately after extended stop-n-go driving, AND/OR, mostly caused if the outside temperature was very hot.
We need more info to better help you, so some questions please:
Did your fan shut within a few to maybe 10 minutes later (dependent on coolant temperature of course);
What was the outside temp, your rough garage temp and how "enthusiastically" where you driving it or did you just get home right after extended stop-n-go (or similar).
Again, if it just ran for a few minutes, shut itself off, not an issue. But if you have had similar temperature and/or operating conditions as this before, but it never ran after shutting your motor off, I would wait until it cools down and check your coolant level. If your coolant level is okay, maybe you have a partially stuck thermostat? [That happened to me just last month on another vehicle.] Of course, your water pump could be starting to have issues, or the temp sensor on your coolant system could have gone south (but I think that is a long shot).
Re your water pump, have you noticed any signs of seepage around it?
Best of luck in getting this figured out, but might be a non issue based solely on its being designed to operate that way, especially if you are having really hot weather.
We need more info to help you (or a smarter member with additional ideas).
I had this happened to me several times too. The first time I waited 5mins by the car and the fan would still kept going so I thought it was a computer malfunction but since I keep a lithium jump starter in the car I wasn't worried about getting stranded. It would indeed shut off after a while just don't really know how long it took. Weather was nice too around 70 degrees.