Did you replace or disconnect the calipers from the lines for some reason?
Whenever I do a brake job, I pull one side apart completely, put a C-clamp on the old brake pad on the piston side, and as I compress the piston(s), I back off the C-clamp slightly to see if the pistons move back out. They should move slightly (a millimeter, maybe less), as the internal seal should be soft enough that they will allow the piston to move slightly as pressure is released (this works both ways). If the pistons do not move slightly after releasing the pressure, the seal is stiff, or there's corrosion or dirt in the caliper that's keeping the pistons from moving freely.
If the slide pins are good, and greased well, this lack of retraction of the pistons will make one set of pads sit closer to the rotor. As you hit the brakes, that one caliper will grab quicker than the other.
I also do the above on brand-new (rebuilt) calipers, as sometimes the rebuild job gets the seal impinged somehow and the piston doesn't move freely.
Other than that, yes, air in one side will make one caliper grab faster than the other, and then the pressure will equalize on both sides.
How do you get the impression it's one rear on one side, and then the front on the other side?