The facility itself is not formally notified when you set up a phone account, and there is no alert sent to staff or administration. The system that handles inmate calls is run by the private carrier contracted to that facility, and account activity on your end is not their concern.
What does happen is that the inmate typically receives a receipt through mail call. It is a straightforward notification that an account has been established, delivered the same way any other piece of mail would be. Depending on the facility and how quickly mail moves, that could take a few days to reach them.
The practical takeaway is that there is no reason to worry about the account setup drawing attention from staff. It is a routine part of how the phone system works, and facilities expect inmates to have people on the outside managing their call access. Once the inmate gets that receipt and knows the account is live, they can start making calls through the number you have set up.
If you are using InmateAid's phone service, the process works the same way. Set up the account, and your inmate will be notified through regular mail. If you have questions about timing or want to confirm the account is active before their next mail call, InmateAid's support team can walk you through it.