The burden is on you to find evidence that an employee's work is slipping. They prima facie have zero obligation to you to justify their off-the-clock activities. Even informing you of those activities I would take as a token gesture of goodwill. In your specific case you have not given any evidence of failure to perform on this employee's part. You've projected your own insecurities onto this third party but not demonstrated any issue actually being present. If this employee's work has objectively suffered then can his ass and get on with life. If his work has not deteriorated then you've got your example right there. Sitting under your nose.

Quit worrying about what this employee can or can't do. Pay attention to what he does or doesn't do.