Q: If I have a problem in my radiator, is it normal that both fans start?

Yesterday I asked you guys about my car overheated when I turned on AC. Today I checked coolant level and I realized it needed liquid. I filled the reservoir and on top of the radiator, but when i was doing that, I noticed that it was leaking at the bottom, so I could see that the problem was that (I guess). Secondly, I started the car and waited for the car to warm up until its regular level (middle). I drived it for awhile and I could notice that both fans were working. However, my AC was off, so I don't know why both fan were on. (I guess the other fan was on because of lack of liquid on the radiator). When I turn on the AC, the air was cool very good and the temperature wasn't going up. I mean temperature kept in the middle as regularly. Of course I just lasted around 4 minutes when the AC on and with the car stopped.

My car has 108500 miles.
My car has an automatic transmission.