My guess is the handbrake cable needs slackening off a bit.
Either that or they've not wound in the rear pistons enough but if that were the case they'd have struggled to get the pads over the discs. Usually they adjust to about the right place once you've wound in the pistons and pumped the brakes a few times.
Not ideal to overheat the pads like that, they might have got very hot. When my handbrake cable froze on (which admittedly was a lot worse than dragging pads), the pads crumbled away from the backing a few months later. Then again, they were smoking. Hopefully they're OK.
I'm guessing you're going to go back to the garage first, but here's how to do the cable, although it makes it seem a lot more difficult than it actually is.
_________________________
2005 Fiesta ST - wrote off
Newman fast road cams, Fusion Fabrications custom inlet manifold, custom exhaust