I stored leftover SMBC that I made for last weekend's cake in the refrigerator. I took it out this morning to use for this weekend's cake, to let it come to room temperature. When I went to rewhip it (using my paddle attachment), it didn't seem to fluff up!

It stayed in sort of that buttery texture form. Should I use my whisk attachment? How long should it take for it to get back to that fluffy form??

Yes, you need to use the whip attachment. (I make this mistake every time!) After that you can use the paddle on low to get some of the bigger air bubbles out. It will probably take a few minutes depending on how much buttercream you're re-whipping and how cold it is.
Good luck!