I don't believe this qualify as spoilers as Asterion's conception is just part of the greek myth. You can just look up the minotaur legend and it should give you the whole backstory from before the trial, what happens after that is then unique to Minotaur Hotel.
You have to keep in mind we are talking about gods here. In the myths, it was common for them to transform into animals and have affairs with mortals, but we should also take into consideration that their parentage may not require to be direct. The myths definitely explicit that Asterion is half bull because of Poseidon, so even if biologic involvement isn't a factor, the minotaur still is one of Poseidon's creations.