Your first paragraph is historically incorrect. The Tridentine Mass was codified AFTER the Council of Trent. In reference to the worldy music you mention, the problem was in the melodies that were employed at the time for liturgical use. Many of these were secular songs with liturgical texts set to them. Also, it seems, from reading some history of Palestrina's time, that there was a problem with the music being so polyphonic and elaborate, that words tended to be obscured by the music.
But on to the point of the "traveling" FSSP priest. I think a couple of weeks ago you kept posting the canon from the Council of Trent regarding priests celebrating outside their dioceses, etc... Does that mean the the FSSP is ipso facto censured?
The FFSP priests are not vagus clergy
There have always been problems with Liturgical Music as our resident expert, Ninenot, reminds us.