No. It doesn't need to be refrigerated. It needs to be kept in a cool, dry place. In fact, refrigeration can be detrimental because, in hot humid weather, it can draw humidity to the powder when you take it out of the fridge, and that's not a good thing.
But, just chunking in a teaspoonful into your coffee may not result in the texture you're looking for. The stuff can be difficult to dissolve.
Hoosier Hills recommends mixing it before hand with a blender and letting it sit in the fridge overnight, then using it like liquid cream.
Also note that it has a different taste from the real stuff, sort of like powdered milk has a different taste.