Passport updation Air India boarding pass

I have got an employment visa at a company in Oman on old passport (ECR) but now i am going with new passport with ECNR. My visa is having old passport number. I was told by travel agency that I have to request the company to send a boarding confirmation to the Air India office at Oman just because I am going by Air India. They say it's not required by any other airlines. Also I have to make them update my new passport details otherwise I'll not be allowed to board the flight... or I will not be able to exit from Oman airport. Please help.. I can't understand a thing...