I've set up a mambership site where a membership type, gives access to a particular category.
This would have to be custom coded. As a workaround though, you could perhaps use the Membership capabilities add-on.
Then assign a specific User Role to each membership plan. This willmean anyone in a specific membership plan will have the user role assigned to that plan.
Then assign the roles to different membership plans.
This will then allow you to send a custom email notification to a specific user role when a new post is submitted.
The alternative would be to custom modify the notify users plugin above to allow it to send to membership users.