Mating season absolutely implies the season during which mating is most probable to occur. There are many animals that follow this behavior despite being able to mate multiple times per year.

One good example from the top of my head is wild boar. They can pretty much mate all year round if they so wish. But choose not to. Their mating season is in spring, which is also the only time you’re not allowed to hunt them.

It’s actually the mother that will keep an eye on her young and make sure they stick to their mating season. If you shoot the mother, her children might just start mating at irregular times and thus bearing young multiple times per year, which isn’t that great considering they are an invasive species in a lot of countries.