This brought a smile to my face as I was thurifer in the years before I was ordained a transitional deacon.
Technically, it can be used at any Mass in the *novus ordo *but, practically, the use of incense is one of the ways in which the celebrant can indicate an increase in solemnity…he can do this in a number of ways such as the use and the extent of incense, the use and extent of singing in the Mass, the use and extent of candles beyond the minimum, the use of torches/incense at the Gospel and at the showings of the Host and Chalice during the Eucharistic Prayer, and so forth.
It never hurts to mention to the priest how much you enjoy being thurifer and that you appreciate the use of incense. It is true, however, that a priest always hears negative things about incense as well…that I can very definitely tell you Sometimes, I have chosen not to use it in light of some requests not to do so – or, at least, to announce ahead of time that incense will be used at such and such Mass.