Back before EFI and fedback carbs, we didn't really have to think much about it...... under decelleration, the air would be diverted away from the exhaust to prevent backfires. As far as vehicles presently being manufactured, I don't know of any with a A.I.R. type system.... though many have electrical secondary air pumps to supply air to the cats to "light them off".
This is a long drawn out way of saying that I am unsure of the operating strategy of the system..... I will say that the pumps were sized for the application.... I will say that many times I have felt and/or heard diverted air coming from the fenderwell mounted muffler.... without giving it a second thought simply because the system was working. Remember that these old systems were, by and large, speed density systems..... The PCM knew the engine displacement, it knew the throttle opening, it knew barometric pressure and intake manifold vacuum as well as engine rpm - more than enough info to establish a reasonable fuel mixture. Taken one step further, the engineers knew the size of the pump and the ratio of the pulleys... (this is assumption and home grown rationalization).... based on this, the engineers know how much air is being commanded where... and adjust programming to suit.
With the level that todays technology has attained..... all I can say is that some of the mandatory courses I take are enough to give you a really good immitation of a migraine.
To indicate how prehistoric our early attempts at feedback fuel control were..... my 1985 F150 4X4 had the EFI 302..... Thermactor pump installed (even in Canada) With a single O2 sensor planted at the back of one exhaust manifold. Chevrolet did the same with their pick ups.... Some had air pumps, some didn't but they all had one single O2 sensor at the rear of one manifold. Dodge muddied the waters even more.... on their pick ups, they went with a "pulsed air" system..... There was no air pump but, instead, there were one way check valves (identical to the antibackfire valves in the GM and Ford systems)that allowed atmospheric pressure into the exhaust .... remembering that each positive pressure wave in the exhaust is followed by a negative pressure wave. The Japs used this system for many years with good success.
Now... if anyone noticed, I always refer to pick ups of all sorts and sizes.... I live in a very small (but growing) town in the middle of the great Canadian arboreal forest..... I don't get to work on cars very often (which is a good thing... I'm fat enough and old enough that you need a stick of butter and a shoehorn to get me in and out of them). As far as early emissions controls, Canada was a redheaded cousin.... in most cases, we lagged behind the US about 3 years. This made for a repair manual nightmare as we searched for anything pertinent to the vehicle we were working on. In other cases, we never did see some of the stuff that was made (and failed) in the states.
I realize that this is a pretty long dissertation... but, hey.... It's Christmas and we can only watch "Miracle On 34th Streeet" so many times....