I haven't seen that for credit credit cards (maybe due to the often-delayed auth cycles), but many debit cards (where charges are done in realtime) where I live do it by default, and my Amex sends you phone notifications if you add it in Apple Pay (even for transactions that were not done through Apple Pay)
Just check your statement before paying the bill, and if you lose your card, freeze it. Also, most credit cards will inform you of purchases somehow, so maybe you need to get a new card.
This is true mostly if it's a magstripe or "card-not-present" transaction, or done online without two-factor authentication.
Otherwise, the burden tends to fall onto the cardholder to provide some form of proof that their card details were compromised.