Generally, HPS bulbs are red/orange spectrum. However, that is not to say that ALL HPS bulbs available for purchase WILL be red spec. Some may be more of a yellowish color, like the red EYE hortilux.

With regards to your cool whites in there, ideally, yes, you would have blue and red specs during flower and/or veg. However, it is not necessary in order to produce great results, contingent on the plants' genetics.