Deeday: Technically there's nothing wrong with what your instructor's saying but most, if not all radio units aren't bothered with that and will happily keep your details and wait for you calling back in 5 minutes' time. Saves you having to do long-winded calls and saves him/her writing out your details again
My view would be to always call up the ATSU if I'm ever going near an airfield, especially a Mil unit where there may be some "interesting" traffic moving at speed in the local area...
Smithy