There are several ways to send out mails:

1. In each plan you have in "Email workflow texts", "Email on first activation" and "Email at each manual renewal" that get sent out once corresponding payments are completed. In there you can use plan and subscription substitutions.

2. The there is the CBSubs Mailer plugin that allows you to send mails at (just after) a basket has been paid, that allows to insert basket-substitutions, such as [PAYMENT_METHOD].

3. Then, you would need to use CB Auto Actions similar to this use-case:
www.joomlapolis.com/forum/255-developer-members-support/243979-revoking-access-in-family-plan#324974

All of them support cb-substitutions and conditions, tutorial is here:
www.joomlapolis.com/documentation/279-community-builder/tutorials/18353-using-substitutions-throughout-cb

It looks like options 1 or 2 are the ones that you are looking for ?

I suggest downloading the CBSubs Manual from our Downloads page below to help get you started.

www.joomlapolis.com/downloads/documents

If you still have questions about setting up CBSubs Mailer after giving that a read please feel free to ask.

The mailer doesn't automatically process. It's a email queue system. You need to run the "Url of cron task to both process mailer rules into queue and then to process mailqueue" URL on the CBSubs > Mailer > Automatic Settings page. This is meant to be used with CRON to schedule email processing.