Nsumba started his career with Ugandan side Villa. He was regarded as one of the club's most important players. He helped the club win the league. In 2007, he signed for Icelandic side ÍBV. He helped the club win the league. In 2010, he signed for Ugandan side URA. He helped the club win the league. In 2015, he returned to Ugandan side Villa. After that, he signed for Ugandan side BUL. He captained the club.