It’s great that you’ve never had an issue and I often have to give out my card number as well, but Target lost like 70 million card numbers a few years back and the problem has continued as stores are individually in charge of the card numbers. Every store that we purchase from thus obtains are real credit/debit card number and typically stores that number in their customer database.
I uncheck the box to “save card” at AliExpress and other stores that offer the option, but in reality this may be meaningless as the card number must be recorded in the transaction record for refund purposes. I seriously doubt that any merchant deletes all digital records of the number after receiving payment, even if they do not “store” the number as a payment option in your user account.
I’ve had multiple instances of credit card fraud ranging in scale from local to international. I suspect that AliExpress is doing its best to protect consumer payment information, but each store that has your card number is a threat vector. Target was not a special case; all merchants are vulnerable.
Some cards offer one-time, “virtual” numbers which you generate and give to merchants as needed. I highly recommend using this option, if available. I used this approach for awhile, but the company abandoned the software and the feature hasn’t worked (for me) in many years. Virtual numbers confuse places like Amazon, however, which “automatically” store each and every card number that you enter and offers them as payment option during future purchases.