They find out the same way most things get communicated inside: through the mail or through a phone call.
If you set up a phone account through a service like Securus, GTL, or InmateAid, the inmate does not get an automatic notification from the carrier. The facility is not going to walk down to the unit and announce that someone set up an account for them. That information has to come from you.
The most reliable way to let them know is a letter. Write down the account details, the number they should dial, any PIN or access information they need, and send it through the mail. InmateAid's letter service is a good option here because everything goes out with InmateAid's return address, your personal information stays private, and the letter arrives within a few days of sending.
If you already have an established way to communicate, a phone call or a message through an approved platform like JPay or CorrLinks works too. But if this is a first contact situation where they do not yet have your number, the letter has to come first.
For commissary deposits, the inmate typically receives a receipt through the facility's internal notification system showing that funds were added and in most cases a last name associated with the deposit. That gives them a clue without requiring you to send a separate message.
The bottom line is that nothing happens automatically on their end when you set something up. You have to close that loop yourself, and a letter is almost always the most reliable way to do it.