When using the Microbe Musher, the Tinkering skill seems to be what increases. But the Cooking skill is what is required to use the Microbe Musher. I haven't noticed any Cooking skill increases, but might have missed it. I'm not sure if the Cooking Station operates the same.
Steps to Reproduce
Enable someone to only Cook in the Jobs list. Cook stuff at Micro Musher, and wait for a skill increase.
This issue has not been confirmed by a developer yet.