Some people on APUG will actually advice against putting the reel inside the stabilizer. In that case you would extract the film from the reel and put it in the stabilizer. It's a bit more messy for sure. I immediately wash the reels with soap after the stabilizer.
With a Jobo-type reel it just means to unlock and take off the upper spiral, turn around the lower spiral above a small bassin with stabilizer and let the film fall into it. Not a mess I suppose.