It does though, regardless of which brake you use. I think this is because the forces are applied at the contact point on the road. It is like applying brakes to the left side of a car, it is going to turn left. The effect is less pronounced in a rear wheel because the braking is naturally limited by the tipping.
Shifting weight might help a bit, but you still need to grip.
Ideally, for an emergency brake you want to use 70% front brake, 30% rear brake, get off the saddle and move your bum as far back as possible.
Safe riding everyone.