Adyen does not automatically update your stored tokens to use the new details. For this, you need to submit arequest for the update to occur.
Expiry date update on card
You submit a payment authorisation request including the card container with all the fields set to null, except for the updated expiry date fields.
New card number issued for card
You submit a payment authorisation request including the card container with all the fields populated with the updated values. The card field should be populated with the new card alias. The shopperInteraction should be set to ContAuth. You also need to include the recurringDetailReference of the old card contract in the request. This will store the new card and automatically close the old recurringDetailReference contract in one action, if the authorisation was successful.