Air injection was introduced prior to catalytic converters and many cars continued to use it in conjunction. The 82 Eagle parts car and the 76 Pacer both had smog pumps, exhaust injection tubes, a relief valve, and an diverter valve. The valves controlled weather the air was injected above the exhaust valves, into the cat, or released. This was done in 82 by the computer, but in earlier cars through a complex series of vacuum amplifiers, valves, and delays.
The biggest hurdle is making sure the exhaust manifold doesn't glow red with too rich a mixture and a constant supply of air, then making sure the cat doesn't do the same. Then it's trying to heat up the cat as fast as possible to get it working, which is the exact opposite problem.
Switching over to pulse-air not only removed the smog pump, but also limited the amount of air that could be introduced and moved the upstream (or cold) injection point out of the exhaust manifold. That prevented the glowing red manifold and made the oxygen sensor a more reliable tool.
The AMC V8 was virtually unchanged after 88, and since AMC had just developed the new 2.5 and 4.0, they hadn't gotten to the V8 yet, so it only got carryover parts. The emissions system is awfully similar to the 1980 258.