Most of tickets issued by airline offices in DR require presenting the credit card. Last Xmas/early January I did around 12 flights on Iberia. Out of those, 2 were bought on Iberia DR. For those I had to present a credit card at check in in Spain. Tickets bought on Iberia USA site did not have this requirement. Mind you, after booking those 2 tickets on Iberia DR I got a clear big red message saying credit card will be required for check in. And you cannot even do online check in if this is the case.
In Barcelona I witnessed a 14 year old with a family member that was denied boarding on Iberia flight to Madrid to continue to SDQ because she did not have the card... it was bought by her family in the DR and she was flying back. She was advised for family member to go to Iberia office to show the card (you can do that, even for more flights that will happen in the future). I felt bad for her because she lost the flight and ticket and in best scenario her family back in DR was hit with a huge change fee and fare difference. Minutes later she showed bank statement showing the charge that was whatsaped to her (it was 5.30 am in Barcelona, Iberia office in SD was long closed) but not even this was accepted. At the end, no she was not allowed to board and missed the flight.
So, better book on airlines' website outside of DR (the airline "localized page").