Trying to show custom post types by “tag”

I’m a front-end developer that’s taking a a stab at the backend, but I’m a bit stuck here.

I’m developing a small tourism website that has custom post type called "Directory" that has the following categories; accommodation, dining and activities.

As it stands I can display the members by "category" on a template, but for the life of me, I cannot sort the members of a custom post type by tag. In registering the taxonomy, I labeled the tags as "type".

I thought perhaps I could simply add a "archive-type.php" file and that would sort the issue our, but no, not working.

Any suggestions?