Collapse and Regeneration
The fantasy animals eat all the prey animals, collapse the food chain, and go extinct. In a few centuries things are back to before the conjunction, perhaps with some of the less fantastical fantasy animals slotting into empty slots in the food chain.
Real world animals are designed to be efficient. Most predator/prey encounters end with the prey noticing the predator and trotting off a few dozen yards. The predator then leaves and tries again later. Most hunts are unsuccessful and end early when the hunter gives up.
Typically the predator (Lion) runs about the same speed as the prey (Wildebeest) and is only just strong enough to kill them. Sometimes they are not strong enough and only prey on the old, the young, and the weak. This creates a predator prey balance.
Fantastical creatures are designed to be large and impressive. Dragons are big and strong enough to swoop over a herd of wildebeest and barbecque the whole herd for dinner, with little effort. They eat all the wildebeest, and make more dragons. But then there are loads of dragons and no prey left. The dragons starve.