Ofer,
Really not an issue unless you soak the carpet and the customer closes everything up and leaves town for a week.
When you get the carpet wet you'll activate spores above the level of the backing, but will also remove the vast majority of them. If the carpet dries in under 24 hours, you will have contributed nothing to the problem. If, when cleaning, you smell a musty odor and want to knock it down, saturate the carpet with an anti-fungal product and rinse. Use whatever anti-fungal product you like.
We clean musty smelling rugs every week and sell an anti-fungal application up front. If the clean and dry rug doesn't smell musty after just washing it (most likely) we don't apply and don't charge for the anti-fungal. Customers are happy-happy.