How this addon prevents the warning issuer's username from being shown is very straight forward. Especially as you have a screenshot of the warning_info template being patched.
The template modification literally just hardcoding a permission check for the current visitor into the template around the username. This checks that the visiting user has the "View warning issuer" permission or the "View warning details" permission. If this check passes, then it shows the username, otherwise the phrase "WarningStaff".