Does being unemployed after a PhD reflect poorly on my advisor? I successfully defended this spring, and made it clear about a year prior that I would not be continuing in academia, with the goal of switching fields and entering the workforce. As part of this, I explicitly said I was not looking for postdocs, and I think I also said I was not willing to do one at all, for a multitude of reasons. It's been just over 3 months since defending, but I have nothing lined up. I've heard that waiting months and months for a first industry position is common, so it doesn't bother me, but I think it's bothering my advisor.

Because a lot of post-graduation roles aren't necessary for my advisor anymore, I'll occasionally receive an email or text message asking me how I'm doing, which includes how my job search is going. These messages have also pointed to potential academic-type positions and the names of postdoc advisors. I thought I was clear, so I wonder where this is coming from. The simple answer is that he is looking out for my best interests, but I'm his first PhD student and he is up for tenure this fall.

Does my unemployment negatively affect his tenure application, or am I over-thinking this?
I'd say yes, you are overthinking it. Any problems you have are not due to him. He seems to be doing what he can, though his connections are, perhaps, not the ones you need now. Your unemployment might be due to any of several other factors, from the economy to how you present yourself. I would continue to thank him for his advice and care, whether effective or not. He might wind up in the future being an effective advocate.

Your lack of employment shouldn't have any effect on his tenure. Not if anyone in the system is reasonable. As I said, any difficulties you have are not due to his inaction or inattention. His tenure is (should be) determined only by his own actions and things he can control. 

On the other hand, tenure decisions are often not especially rational. Sometimes they are just determined by personalities. Other times by the perceived need of the institution at that moment.