Everything happens on the Subscription page.
Upgrading takes you to a secure Stripe checkout. Your plan switches once Stripe confirms the payment to us, usually moments after checkout, and the page shows honest progress until then. Cancelling keeps your plan active until the end of the period you have paid for, with a note showing when it ends; after that you move to Basic. You never lose time you have paid for. Switching down, Ultimate to Pro, works the same way: it takes effect at the end of your current period.
Changed your mind? "Keep my current plan" undoes a pending cancel or switch before it happens. Your subscription payments, including any refunds, are listed on the Billing history page.