I've never ordered from Woodland Hills Pharmacy, so I'm not sure. From other pharmacies I've ordered from, it depends if the medication is in a liquid form, already dissolved for you, or not. If it is in liquid form, then yes it needs to be refrigerated. Other medications that you reconstitute yourself, by adding to water/saline, I don't believe you need to refrigerate. Some medications that I had reconstitute, I also had to refrigerate. Others I didn't.
However, I've had bad experiences with all of these pharmacies and made me order overnight shipping when I didn't think it was necessary. Call them and ask why it's necessary and if it really is. It may be a liability or regulation thing.