When someone Likes one of your posts, only the people allowed by the initial visibility setting (the one you set) will see the Like.
However, when you tag someone, the post may go on their Timelines. From here, things get a little tricky. The first check is against the visibility setting you assigned to your post.
If you set it to
Friends Except Acquaintances, then the friends of your tagged friends can also see it (except your own acquaintances, as applicable), UNLESS you also uncheck the "Friends of those tagged" box after clicking the
Custom... option. This checkbox can also be unchecked globally for all future posts from
Privacy Settings under the "Control Your Default Privacy" section. Simply select
Custom, then pick
Friends and uncheck the box.
Back on topic. The post will NOT be visible to your tagged friends' friends' if you set visibility to either of the following
- A more restrictive group than
Friends Except Acquaintances) (eg.
Close Friends or
- A custom group/list (it doesn't matter if it's a list that encompasses all of your friends — what matters is that visibility show "Custom").
Do note that "Friends of those tagged" only applies to
Friends Except Acquaintances. Whenever you restrict the initial audience, it's as if you unchecked that box as well.
Still with me? There is then a final check in how your tagged friends' configure their own
Privacy Settings to allow their own friends to see the posts that they are tagged in. This setting is under
Timeline and Tagging, "Who can see posts you've been tagged in on your timeline?"
This all seems rather complex, but I think it makes sense. The general philosophy is that by default, Facebook tries to share your posts as broadly as possible, but as soon as you add restrictions (such as sharing with a smaller group than all your friends), then it will do what it can to respect your restrictions.
Public, this setting does not make the
Friends of those tagged checkbox available because it assumes that it is checked. Your tagged friends' setting for who can see their tags on their timelines still applies.