the problem here is that you've added the function call to the admin_init
hook. The admin_init
hook is only triggered when the user accesses the admin area, but you're submitting a form here, an action taking place on the front-end of your site outside of the admin area.
It's a simple fix :-) Just use the front-end initialization hook instead — init
Also check out this reference for the actions that are typically run when a page is loaded, on the front of your site and the admin area: