People did not hunt tigers for "most of our evolutionary history". In fact, it's quite recent that people have hunted tigers at all, and even then it's more of an outlier than a standard practice.
Tigers are difficult and dangerous to hunt, and they're not healthy to eat regularly, nor is their meat particularly attractive (despite the named "tiger meat", which is actually raw beef).
Furthermore, contrary to mass media depictions, tigers rarely attack humans unless provoked, and they avoid human settlements as well. So even as a matter of safety and defense, hunting tigers is a rarity.
Until, of course, you start destroying large swaths of their habitat by mass-clearing old-growth rainforest in order to produce enough food to keep up with the usurious demands of a colonial occupier. At that point, yes, you do start to combat tigers more directly.