They should be getting a basic email from PayPal at whatever email they use during checkout, but it could be easy to miss.
Depending on which type of button integration you are working with I would suggest that you use either IPN or Webhooks to generate and send your own custom branded email notifications.
This would allow you to not only send email notices when orders take place, but also if/when a pending e-check clears, a dispute is filed, a refund is processed, etc. All with your branding, links to featured products, discount offers, or anything else you want to include in those emails.
You could also automate posts to social channels, updating your own database, send your own internal team email notices, etc.
If you don't have a developer available to do this for you feel free to reach out to me directly and I can get you an estimate on doing this for you.
Hope that helps!
Angell EYE - www.angelleye.com
PayPal Partner and Certified Developer - Kudos are Greatly Appreciated!