I agree that you will get a darker color printing the trans blue over the red, but not the reasoning behind it. Red is tonally darker and will create a dark base for the trans blue overlay. So, in essence, he would then be printing dark to light. Just me two cents.It looks like you are printing in the wrong order. Offset printing is dark to light, but in screenprinting you print light first, then dark. So you should print your warm red first, then your cyan. The purple you are getting is partially because your red is sitting on top of your cyan and not blending well at all.
good lord, gigposters is dropping excellent advice on all manners of print planning, client managing, awesomeness that is supposed to be top secret. It's like I've woken up outside of time and place.