My first transactions happened today but they appeared on my regular Visa card and not the Apple Card on my iPhone. What should have happened?

Did you do the transactions in a store? If so, was Apple Card set to be the default card for Apple Pay or did you manually select the Apple Card as the card to be used before each transaction?

See the following information about using the default card or using another card ( from Make purchases using Apple Pay - Apple Support )

Pay with your iPhone

1. To use your default payment card:

• • If your iPhone has Face ID, double-click the side button. Authenticate with Face ID or enter your passcode.
  • If your iPhone has Touch ID, rest your finger on the Touch ID sensor.

1. To use a different card, tap your default card to see your other cards. Tap a new card and authenticate.
2. Hold the top of your iPhone near the contactless reader until you see Done and a checkmark on the display.

Also see the following from Manage the cards that you use with Apple Pay - Apple Support

Go to Settings > Wallet & Apple Pay on your iPhone or iPad, and scroll down to Transaction Defaults. Tap Default Card, then choose a new card.

On your iPhone, you can also open Wallet, touch and hold a card, then drag it to the front of your cards.

It sounds like you are asking about Apple Cash instead of Apple Card. Apple Cash has the large word "Cash" at the top left of the card in the Wallet. The amount shown on the Apple Cash card is the credit balance, not recent transactions.

If you tap on your Visa card in the wallet, it will show any recent transactions.

If you tap on your Cash card in the wallet, it will show any recent transactions.

My previous reply about how to select which card is to be used when making a purchase with Apple Pay and how to change the default still apply.