They don't develop this equilibrium "instinctively" (something exclusively inside them) but they do "naturally" (helped by the environment). Now the reindeer weren't really in their natural environment, they were put in very constrained, special conditions, with little flexibility, little time to adapt, and no ability to shape that environment. The environment forced them to adapt and lower the numbers, and eventually wiped them out with what was also probably a fluke. They were still 50% more individuals than when they arrived but no viable reproduction path ahead.

This was an extreme example. Put humans on this type of island and you'll probably end up with them dying out just the same, despite our tendence to radically change the environment to survive. After all that's why the reindeer were there, so humans can survive absent a constant lifeline from civilization.

Humans, and viruses to a degree, are much better at shaping their environment and adapting faster to what's thrown at them to compensate. The instinct is to change whatever possible of the surroundings to survive and thrive.