If this tab opened by itself while you were setting up Mind My Money, that was the app checking it can drive your browser — and it can, because you are reading the proof.
This is the same mechanism Mind My Money uses when it goes through a real month: it opens your bank and card portals in a browser on your own Mac, the same way you would, and stops for you at every real login. Nothing was fetched from this page and nothing about you was sent to it. You can close this tab — the app will carry on by itself.