This trick (called dynamic currency conversion) is commonplace in touristy places. The card scheme rules say that the customer must be given the option to choose which currency to pay in, and if not, the customer gains chargeback rights with the credit card company for the difference between the amount paid and the amount that should have been charged.

Paying in your card's currency is virtually always a bad idea; the rate I have been offered has always been worse than what I was eventually charged.