When attempting to change NameTagVisibility values, no changes are seen. Whether it is with the vanilla commands or through a plugin.
Based of the API this should work, and doesnt. When adding players with the vanilla commands to a team with NameTagVisibility set to Never it still has no affect.
If this is executed in a vanilla implementation it works just fine. Just not the spigot or craftbukkit implementations.
No noticable change can be found when changing the enum values from NEVER to HIDE_FOR_OWN_TEAM or HIDE_FOR_OTHER_TEAMS.