Air-bags deploy according to what force the crash places on the car. There’s no hard and fast rule to this, because no two crashes are the same. So, the sensors that tell the air-bags to deploy take into account the amount of deceleration involved and compare that with a threshold reading to decide whether to deploy the bags or not.
A car travelling at very low speed that noses into a wire-rope barrier, for instance, may not decelerated sufficiently for the bags to go off. But the same car, travelling at the same low speed that is hit by a moving car coming the other way, is much more likely to deploy its air-bags.
And just because the side air-bags have deployed in a crash, doesn’t necessarily mean the front air-bags will also be deployed. Sometimes the front bags will go off in sympathy with the side air-bags, but if there was not sufficient forward deceleration, the front ones should remain intact.
However, the tule of thumb is this: In Australia, air-bags are designed to deploy at speeds above about 25km/h and, in the case of front air-bags, in any impact within roughly 30 degrees of the car’s direction of travel at the time.