According to the PBG website, the kit no longer comes with Klusons as standard, so the headstock holes are probably drilled for the larger diameter standard tuners. Measure the tuning hole diameter and if it's around 0mm then you'll definitely need the adapter bushings King Casey linked to. The vintage tuner bushings are around 8.6mm diameter so if the hole's any bigger than 8.5mm, it's adapter bushing time (unless you plug and re-drill the holes to a smaller diameter hole).

There's nothing else that's holding the bushings in apart from friction between the bushing and the wood. It doesn't get any better with the tuner posts inserted (and using the tuners will probably loosen the bushings further. A very slight looseness can be compensated for if you are using a clear lacquer on the neck by running the lacquer into the post holes to reduce the diameter, and a small dab of PVA or Titebond will help keep them in place.