In last night's debate, it is widely reported that Trump got the best of a back-and-forth with Ted Cruz over Cruz's linking Trump with "New York values." In a technical sense that is perhaps true, Trump's invocation of 9/11 heroism of police and firefighters was a good riposte.
Cruz, however, knows what he is doing. New Yorkers (city dwellers and suburbanites) are widely disliked as pushy, rude, and antagonistic. Traits valued by New Yorkers but widely detested by the rest of the country, particularly by Southerners like those in SC. Reminding folks Trump is a New Yorker is a way of reminding them of his less attractive features.