Being a cabal and not an organization, Tribunal is still idealogical to some degree. It's about more than just staffing a police station.

A core part of Tribunal is not just protecting people, but making sure you don't cause harm to innocent people in the process. That's why there are consequences for making mistakes and (quality) Tribunal leadership usually emphasizes not doing things like placing flags unless you're absolutely sure.

Given that, I think it's natural that the cabal would have a hard time trusting evils to perform their duty willingly and well.

All that said, I think it's important to remember that evils can still get into Tribunal. It's harder, for now, but still much easier than a lot of things. Likewise, once you're in (regardless of your alignment, in fact) you can start vying for leadership and eventually influence policy yourself.