Reflex (induced) ovulators are reasonably common in mammals (mountain hares and various carnivores, for instance), so that part of your creature's biology is not a problem. It is in response to copulation, not to female orgasm.
(I confess to complete ignorance as to which mammals apart from people and lab rats show female orgasm).
The male side is more tricky, because sperm production and maturation takes time. Over 60 days in humans. So your males have to spend a couple of months preparing their sperm before the rut.
Heightened sex drive in males during the breeding season has real world biological precedent. For instance:
Various species of hamster that hibernate, shrink their testicles and shut off their hormone production in winter. Then switch everything back on again and regrow their testes to full size ready for the breeding season. So your creature could be like the hamsters, except without the hibernation. Day length could still be the cue for doing this, however. The autumn equinox arrives, days get shorter and all the guys' lose interest in sex as their hormones dwindle away and their balls shrink.
Male elephants go into a 'musth' period, which is a (sort of) male heat. Hormones levels go screaming away up. The male gets aggressive and hyper interested in sex and male-male dominance struggles compared to its normal self. Musth is more complicated than that, because elephant bulls mate when they are not in musth (and sometimes attack rather than court elephant cows when they are in musth). But you could use it as a basis for your creatures.
Or combine the hamster and elephant biology to have a creature which shuts off hormones and shrinks testes, then goes into musth when it switches them back on.