Capabilities and CPT's

I have a custom post type I need to allow all users (subscribers) to edit, create and do all that on their own posts for that specific post type.

My post type is for levels, and I need everyone to be able to create them, edit them, publish them and delete them (only their own obviously) and was instructed to use this plugin to handle that, but I can’t get that stuff working.

I have custom permissions that show up in Membership role editor (sort of):
They show up as:
edit_
edit_others_
and so on, but they are registered in the plugin like this:

$capabilities = array(
 		'publish_levels' => 'publish_level_entry',
 		'edit_levels' => 'edit_level_entry',
 		'edit_others_levels' => 'edit_others_level_entry',
 		'delete_levels' => 'delete_level_entry',
 		'delete_others_levels' => 'delete_others_level_entry',
 		'read_private_levels' => 'read_private_level_entry',
 		'edit_level' => 'edit_level_entry',
	 	'delete_level' => 'delete_level_entry',
 		'read_level' => 'read_level_entry'
	);

and when I try to grant them for admin (me) and Subscriber, either myself or my subscriber test account have access to them.

What am I doing wrong?

https://wordpress.org/plugins/members/