No, it could be used at every Mass even daily, but on the other hand your priest is mistaken in that incense is not actually required for solemnities either. The GIRM states:
276. Thurification or incensation is an expression of reverence and of prayer, as is signified in Sacred Scripture (cf. Ps 141 [140]:2, Rev 8:3).
Incense may be used if desired in any form of Mass:
a. During the Entrance procession;
b. At the beginning of Mass, to incense the cross and the altar;
c. At the Gospel procession and the proclamation of the Gospel itself;
d. After the bread and the chalice have been placed upon the altar, to incense the offerings, the cross, and the altar, as well as the priest and the people;
e. At the showing of the host and the chalice after the consecration.