There's an old fortune-cookie game that we play whenever we go to a Chinese restaurant. Special relativity is like that game. The meaning changes completely if you don't nail down the wording. There is no absolute time and there is no universal common start time.
Time is very specifically and interval between the observation of two events.
So its really a special case of rule two. This is the same as saying that during the interval under consideration, neither of the oberservers can have any way of telling by any experiment who is moving. This is the basis, and the solution, of the so-called Twin Paradox. That's not so here. If nothing else, such wordy rules should give you an idea of why we use math instead.