Is a downloaded OS X installer from the App Store tied to my Apple ID?
If by reinstall the OS, you simply mean reinstall it and not run first-time setup, the resulting installation will not be associated with you in any way.

If you intend to run first-time setup, obviously do not login with your Apple ID during that process, and of course don't input any personally-identifiable information either.

There is metadata in a receipt file in the installer file itself that is associated with your Apple ID. That is not transferred to the resulting installation, though.