You can also fly it without the staging tube. I have two flights in mine now (24mm Tiny Tim / 18mm WAC) and in both instances the WAC motor lit without an issue.
The staging tube may help with limiting the amount of scorching that the top of the Tiny Tim booster and those wooden dowels that are part of the interstage coupler experience. I had to rebuild the paper cone at the top of the Tiny Tim booster after the first flight, it was more than a bit singed (and yes I had soaked it with CA per the instructions). The rebuild uses a layer of 3/4 oz fiberglass cloth to try and make it a bit more flame resistant...
Be sure to check the fit of the booster around the WAC motor tube after each flight, I've found that the black powder residue can make the slip-fit, less so.