Yes, it is normal for some people to experience that redness. If you are concerned about this you can go to your doctor and ask if you could possibly be allergic to some ingredient in the foods you are eating, that cause the redness.
It really isn't an allergy when hot or eating spicy foods though. It is how our system reacts like a flush if you will. Different skin types, skin colors all react differently.
My husband and son get all red, I get a slightly runny nose.