Personally I don't it is written down as a 'law' anywhere. From my IR test I seem to recall that all you had to do is establish on the inbound course and reamin within the defined protected area for the hold (ie at the correct speed).
If you go over the fix and then start your rate one turn onto the outbound leg, then I don't see why you have to time that. In my mind the only bit where you need to time is your outbound leg, so start your watch at the start of the outbound leg, which to me is wings level or passing abeam the holding fix (whichever the later).
I suspect the instructor 'just preferred' the method he was advocating. I stand to be corrected though, especially as you seem to be talking military aviation and all I did in the military was run round shooting at things with a rifle.......!
PP