Hi rmagenheim,
Recurring transactions will be based off the information in the template you have saved. Updating a customer's information will pull up the new information when you manually create a new transaction, however it will not update the address on the template.
If you click on the gear icon and choose Recurring Transactions from the dropdown you can edit the information in the template so future transactions will automatically be created with the address from the template.
Also under the gear icon is the choice for Feedback, and it seems like a good idea to have some acknowledgment that a customer whose information you updated has recurring transactions, and a way to update those templates more easily.