For virtual rewards like air miles, cash rebates and points, the rewards will be automatically credited to your credit card accounts upon meeting the relevant spending condition.
For cash coupon or voucher, it will be mailed to your correspondence address after meeting the fulfilling condition.
If your welcome offer is an object like a luggage, a fulfillment letter / redemption letter is what you will receive my mail, and you will need to redeem the gift with the letter in specific venues.