Aer Lingus will charge in the currency of origin

So if your first flight starts in the US it will be in USD, if it starts in Ireland, EURO and if it starts in UK, GBP. For any US originating flight I have always been charged in USD.

The currency of payment is shown on the booking confirmation email.

It is likely the transaction was processed in Ireland which is completely reasonable as you are booking with an Irish airline.

If the base amount shown is what the tickets cost then your grievance is with your credit card company who added the charges. The retailer has no idea what charges may be. It would appear you have got stung by a shady practice to charge a foreign exchange handling fee even though no conversion occurred.