Wecome to the World of Golf guys.
Most if not all Private Members Clubs give preference to the Club Captain and the Pro Staff. The Pro may be giving a Playing Lesson and needs to be able to get on the course (it is his living).
Then because the Public Courses are run through the Pro-shop the Pro also gets preference there.
If the Pro had walked onto a Tee and said that he was going ahead of you, then I would have said you had a case, but you say you saw "Them" on the 12th and took a couple of holes to get close enough to talk to them.
Here in the UK the standard rule is that it is OK to 'jump in' if there is a clear hole behind, like going from the 4th green and teeing off down 12 is OK if no one is playing the 11th.

The Pro's manners may come into question but nothing else.