It has nothing to do with rain water, but rather atmospheric conditions when it rains. Septic tanks rely on anaerobic bacteria to break down waste. Their activity emits foul smelling gases. Normally, these gases work their way up the main drainage line to the venting system and out up through the roof.
Normal atmospheric conditions carry away these gases unnoticed. In certain conditions, the air over the roof containing the foul smell is denser than the surrounding air. It then slides down the roof slope onto the ground level where you can detect it's foul payload.
There's no a lot you can do about this. You could install a house trap with a vent that could be directed somewhere where odor release would be less objectionable. The house trap would prevent odors from coming out on the roof, all odors will go out the house trap vent. Traps prevent the passage of gases past the trap, but they must be vented or the water gets siphoned out and the trap no longer blocks gases.
Depending on the tank location, you could directly vent the tank. Most odor will come out at the tank instead of the roof. Tank venting in some jurisdictions is actually required. If the tank is near areas you spend time in, this would not be a good solution.
Septic tanks smell. All you can hope to do is manage where the smell is released.