It's not exactly normal, but it's probably a common enough experience in the US with 120v circuits and 15A breakers. Especially if in an old building with imperfect wiring causing excess resistance.

Many devices also operate less efficiently in high heat. If the AC unit is on a circuit with other devices, it is possible that the influx current when starting the AC unit trips the breaker. One might even be able to get away with 2 AC units on a 15A breaker as long as both compressors never start at the exact same time, but cause a trip when then kick in together.