You do not need the customer number. You are confused because there is also a “Swiss Pass” product that is targetted at the locals. “Swiss Pass” is not the same as “Swiss Travel Pass”.
If you created an account (without customer number) on sbb-tickets.cc and then bought the Swiss Travel Pass you will have it in the app on your phone if you log in with the same account.
If you however did not create an account prior to purchasing the STP you are not able to add it afterwards. However as long as you can show the QR code to the conductor one way or another you are fine.