If it was indeed spontaneous, I’m surprised that the Director of Music went along with it by providing the music. I personally would never agree to play ‘Happy Birthday’ on the organ! If the priest really felt that he had to mark the occasion in some way, he could have mentioned it during the announcements or if it was a particularly significant birthday, it could have been printed in the Parish Newsletter.
I have been asked for worse, however - and by priests! At the end of an annual novena given by the Redemptorists at our cathedral some of the mission priests feel we should sing certain well-known traditional Irish songs! I have always refused saying that it is inappropriate & that even if I had the sheet music I still wouldn’t play it! A fellow organist, at a special children’s session of the novena, was asked to play some tunes that the young kids would know - “Barney” etc…
I’m not really sure what you should do at this stage. I know once is enough, but if this really is an isolated incident, as Joe said, there may not be a huge cause for concern - if it becomes a regular occurrence, then definitely speak to the priest…