The setting "Admin Approval for Course" is for the instructors, that instructor can directly create a course and publish the course or they can only create a course but admin has to approve the course/publish the course in order to show it publicly on the website.
But when you purchases a course then actually you are purchasing the woocommerce product because the products are only sold and purchased not the courses, courses are only connected to the products to show the pricing and once the product is purchased wplms gives access to the course.
When you purchase/order a course/product through woocommerce checkout page then you have to go to wp-admin->woocommerce->orders, and approve the order, refer:
http://prntscr.com/bsu68f
If you wish that the orders should be automatically approved then try using this plugin:
https://wordpress.org/plugins/woocommerce-autocomplete-order/
Let me know if this helps.