Your credit card statement/ bank will copnfirm the US$ amount charged and the rate of exchange applied. Or possibly that you have been charged in € directly.
Assuming the US$ amount in not the same as on your email of confirmation, report this to your credit card company immediately and start building a case to protect yourself. Then call the tour operator again, and let them know that you will instigate a "charge back" procedure with your credit card company if they don't honour the agreed "consideration" agreed contractually.
I have come up against this a number of times, where systems will re-price against a local market rate, defined by country of residence. I have always won, but it is a total headache.