Are you sure that when you set your tree as private, that you also clicked on the box that marks the tree as unsearchable?

The following is from the settings page:

"Private Tree

This setting allows you to keep your tree "private" so that other users cannot view the contents of your tree.

What does "private" mean?

Limited information about deceased individuals in your tree (name, birth year, and birthplace) will still appear in Ancestry search results. However, no one can view your actual tree without your permission. If another member wants to view your tree, they can contact you anonymously through our Connection Service to request more information. Keep in mind that these individuals may also have helpful information to share with you."

THEN:

(A Check Box) "Also prevent your tree from being found in searches"

Note: Although your privacy setting will change immediately to public or private, it usually takes about a month for this update to be reflected in the search index.