I didn't provide my credit card during the call.
They charged me on the credit card I used during the initial reservation but definely didn't give it during the call.
I asked him to check the price on the 18th, December, said I didn't want to pay an additional fee as I had already paid a price difference earlier and asked him to explain to me the reason for this "flat fee". I also asked him for the possibility to modify the reservation online so that I can "check by myself" which one best suits me but he refused.
As I said, he then put me on hold and I hung up