The Norse peoples who colonized Greenland had better technology than the Carthagenians and yet they had a heck of a time with the natives (actually the "natives" of Greenland were there second, the Norse were there first). So I'm not sure if the Carth descendants can do much better in a higher density populated place like Cuba. Bermuda was never inhabited by Native Americans, so better chance there, however in OTL it took 100 years from first being discovered (1507) to being settled (1609), so I'm not sure how easy it is to settle without nearby places being able to send supplies and help. Oh, and hurricanes occur, one bad one can make it unlivable and wipe out methods of leaving. If Bermuda is colonized, then "Virginia" to "Florida" discovered, perhaps they can trade and learn maize cultivation. New York Harbor would be a perfect Carthagenian playground, exactly what they like to see, you could see multiple city-states erected complete with temporary alliances and wars play out in the Harbor as seen in the Greece among the Greek states, with the Hudson Valley and Iroquois being influenced by their technology and customs and ideas of Empire, you might see a more powerful Iroquois form, or the nearer Algonquin tribes might stop the Iroquois from forming in the first place with the help of the Carthagenians. Either way, just as the Hellenized Macedonians learned, assimiliated, and eventually subjugated the Greek states, the same will happen with the Native Americans to the Carths. A Native American empire will form in the Hudson Valley, and take the Harbor, then move west along the Mohawk Valley, and there might even be an Alexander or Chengis like figure who attempts to go as far as he can west in the Ohio Valley and eventually (maybe upon seeing the great Mississippi River?) has to turn around or dies.