Both. The sequence is technically off on that detail, but someone who knows their stuff should know better than to complain about it. The simplest fix is to just say that this is a special custom half-silvered mirror that has these phase shifts.

I was going to say that the cleanest fix would be to make the math right, but looking at the math, it seems that the real math is so much messier and harder to explain (half-silvered mirrors invert or not based on which side you half-reflected from!) that getting it right would muddy the waters far more than using your power of arbitrary setups to make an idealized apparatus.