Culver played the 2011 season with Staten Island. In 69 games he hit .250/.323/.337 with two home runs. In 2012 he played for the Charleston RiverDogs. He hit .215/.321/.283 and two home runs in 122 games. Culver decided to stick to batting right-handed rather than switch hitting prior to the 2013 season. He started the season back with Charleston. In August he was promoted to the Tampa Yankees. Overall he hit .248/.322/.362 with nine home runs. He remained with Tampa to start the 2014 season. In 132 games for the Yankees, he batted .220/.298/.303 with 5 homers, 48 RBI, and 12 steals, playing 130 of the games at SS while serving as the DH the other two.
His father is currently serving nine years in Attica Correctional Facility for attempting to set his family's house on fire in order to kill Cito's mother on March 22, 2008. He was later diagnosed with bipolar disorder. By terms of the plea agreement Culver can have no contact with his father.