I don't understand the term "melody" in this context. Isn't the tone of the day set for Orthros and Vespers? The booklet we use tells us the tone of the day and which tone in which to chant each hymn. I understand for the Liturgy, the melody may refer to the arrangement of our Western musicians, like Gallos, Desby, etc.
Even thought the priest is in charge of the service, my experience is that the Chanter (or Choir Director) chooses the music they chant/sing. Without attempting to act as if I know what is going on in your parish, sometimes priests direct the chanter when they don't think the Chanter knows the tones or the order of the services, or if they are particularly proficient and interested in executing Byzantine music. Similarly, there are priests who don't know the music all that well, and are happy to have the Chanter handle it.