At a guess I'd say the cams broke for lack of lubrication to their bearings. There are oil passages through the gasket to allow oil, under pressure, to move from the block into the cylinderhead for distribution to the cam. Installing the wrong gasket could block these oil passages and after some miles the cam would melt its bearings and seize.
Second possibility: Upon reassembly the cam was not synchronized with the crankshaft - not correctly timed - allowing the valves to be hit by the pistons. This happens when the timing chain (between the crankshaft and camshaft) breaks. Big expensive mess - some new valves, valve guides and camshaft. This horror would be almost immediately evident when the engine was first started.
Third possibility (speculative): The timing chain is kept under tension by an oil pressure actuated ratchet mechanism (or similar). To remove the cylinderhead the chain must be slackened - tension removed - by releasing the tensioner. I speculate that it could be that the tensioner was not reassembled correctly and the chain was untensioned - floppy - perhaps even to the point of jumping links on its sprocket and so losing the correct valve tining as described in Second above.
However it occurred, it's an unhappy situation between you and the repair shop that installed the head gasket. The camshaft didn't just happen to break independently of the head gasket's replacement, IMHO.