Yes, once set up, the ReferralCandy app monitors and detects* successful referrals automatically. However, it may take a couple hours after a purchase for the platform to run through all the necessary verification checks so it isn't instantaneous.
*Note: For platforms with specific plugins (e.g. Shopify) the ReferralCandy app obtains information directly from the platforms. The unique referral link together with the information obtained from the platforms enables the app to track sales that come from referrals.