I am a Idaho resident, if I purchase a non-resident deer tag on or after August 28, will it be valid for both the whitetail seasons and the regular deer tag seasons?

You must purchase the type of deer tag you want.  If you want to hunt for white-tailed and mule deer,  purchase a regular deer tag, which is valid for either one (as long as the unit you are hunting is open for both).  If you only want to hunt for white-tailed deer in one of the later seasons, purchase a white-tailed deer tag.