It depends. Mammals do go into have estrus and the higher primates do have periods, but that's because that if you go back far enough in the evolutionary chain, there was some ancestor for whom it was advantageous to develop the ability to have fertility cycles.
But that doesn't mean that it would be the same for aliens. Yes Ausar might be dog-alien aliens and Kaithrit might be cat-like aliens, but the key point here is that they are aliens. Biological function A doesn't always mean biological function B would be the same. I mean, if it did, Anno shouldn't be able to get sweaty when she exercises and would have to cool down by panting because dogs don't have sweat glands (and not the fun kind of panting). By the same token, the Tove might have an avian appearance, but they reproduce in a manner more like plants. The point is that, alien species might reproduce, but it's not going to be an exact facsimile of how Terran's reproduce.
But at the end of the day, this is a porn game and periods aren't a thing. Fertility cycles do exist, after all, pregnancy is an aspect of the game, so Occam's Razor would tell us that there are probably everyday items that lessen the impact it has on women.