"animals" is a really broad designation. Elephants, for instance, can detect subsonic signals and they have big feet, so they might be more inclined to detect the primary wave of an earthquake. But then again, a primary wave traveling through the air will not reach the elephant as fast as the secondary wave traveling through Earth.
Note that the "instincts" of the animal aren't much different from ours. Once we detect a catastrophic event we run, freeze, etc, whatever our adrenal response is.
The significant part is the detection, not the instinct. Do animals have the physical apparatus necessary to detect the signal? That should be the question.