Which paper are you using, Charlie? I use TruePix and have never had the staining that you're showing above. Sure, I get the staining from the camera aperture, but that's to be expected as the dye flows through the hole on to the jig, but not the staining anywhere else. It could either be that your printer is laying down too much of the ink/dye or that your paper is too thin and so it's escaping somehow. I suppose the other explanation could be that you're not pulling the heat tape tight enough, so it's allowing a tiny gap where the sublimating dye is able to escape to.
I did buy a couple of iPhone 4 and iPhone 5 jigs from someone and they came stained, but I used water and wire wool to get rid of it. It looked like years of build-up, though. I've had runs of 100+ cases at a time with no offsetting whatsoever, and I never wash my jigs. So yeah, it's likely either too much ink/dye being laid down by your printer (I use an Epson 7600) or the paper (again, I use TruePix).
Hope this helps
M