old man: Just as you are moida that a shul must adhere to the shul’s minhag in havara, so too in the case of the OP’s Yeshiva they are correct for insisting that they adhere to the Yeshiva’s minhag in havara.
So the yeshiva is now a Sem teacher, making things up and saying they are assur so that the students should follow what they personally think should be done?
You are being Motze La’as on the Yeshiva! If it was a minhag, they would have said so, not said the students are not Yotze.
(And yes, this is common from stories I have heard from sem girls, so it is not Motzi La’az. I have just never heard this behavior happening in yeshivos, where they respect Halacha).