Mentor

Mentor seems to play an important part in the ritual. He probably is the one who actualy performs it. Mentor is the wise man who mentored the youths like Telemachos to maturity by educating them and brings them to the test. Mentor performed the test by bringing the nineteen year olds up and down to Pylos. A risky operation without adults (except for Mentor himself):

Odyssey Book 3 line 328-330 Barry B Powell
Odyssey Book 3 line 12-13 Barry B Powell

Mentor and his pupils arrive at Pylos

For I alone among them am the older man. The others are younger men who follow in friedship, all of a like age with great-hearted Telemachos.

Except for Mentor all are at the same age, they all become matured at Apollo's Day. They are Mentor's pupils. And the trip up and down Pylos is their exam. When Mentor and his pupils disembarked in Pylos Athena (Mentor) says to Telemachos:

Telemachos you have no need to be embarrassed, not a bit.

It is obvious that Mentor is the Tutor and he also is going to perform the ritual for at least the maturing men who travelled to Pylos with him.

Mentor is a wise(Athena) man, Mentor is the priest of Apollo!