When either of the toilets is flushed, we can hear the water run in the master shower drain. This is only when the toilets are flushed. Not when water is used anywhere else in the house. Why?

This has little to nothing to do with the fact you have a septic. Sounds to me that your vent stack is plugged and the toilets are trying to vent via the shower drain. Can you get to the shower trap area? Do you know where your vent stack terminates?