In the popup notification, it tells you that you'll be notified, but it doesn't tell you how. User talk page? Email? Echo notification?
Providing that explanation in the dialog itself seems excessive. This is basic information, so perhaps it should be at Special:Newsletters, right under the header.
Currently there is no intro text, and the text of the dialog is
You have been subscribed to "(Newsletter name)" newsletter. You will now receive notifications when new issues of this newsletter are announced.
Instead, we could have an intro and make the dialog shorter:
This is a list of newsletters registered to this wiki. Subscribe to a newsletter to receive a notification when a new issue is announced. You will receive notifications via web or email, according to your preferences.
You have subscribed to "(Newsletter name)".
If we apply this change, then the Unsubscribe dialog should be changed as well:
You are no longer a subscriber of "(Newsletter name)".