I'm the developer, so take this with a grain of salt. But this plugin works great with or without Paid Memberships Pro. You simply enter your MailChimp API information, save, and then assign any of your MailChimp lists to be subscribed by your users. If you have PMPro installed, you can set different lists per membership level.
When users register for your site (or change levels), the plugin will move them into the appropriate MailChimp lists.
You can enable or disable the double opt-in. If enabled, users will receive an email to confirm their subscription to the list. If not, they are just added to the list. Be careful if you don't use double opt-in, as too many "spam" ticks on your emails could result in penalties against your MailChimp account. However, if you have a very clear membership site and users expect your emails, you don't need to bug them with yet another confirmation email.