Here is a possible way the two cooling systems are coupled:
With the AC on the vehicle has to reject additional heat to the atmosphere (sourced from the cabin).
This heat is rejected through the condenser, which is usually right next to the radiator.
The end result is that the coolant in the radiator is hotter than before, resulting in higher cooling system pressures. At a high enough pressure this can send some of the coolant to overflow, resulting in loss of coolant.
This behavior could be due to a number of factors, such as a radiator cap that isn't holding its rated pressure, or a clogged radiator but it could also occur just due to extreme outside heat.
I find this occurs on some of my vehicles on extremely hot days (45+ °C); I just need to top it up afterwards and make sure the level doesn't go too low.