Heavy-metal free ternary semiconductor nanocrystals are emerging as key materials in photoactive applications. However, the relative abundance of intra-bandgap defect states and lack of understanding of their origins within this class of nanocrystals are major factors limiting their applicability. To remove these undesirable defect states which considerably shorten the lifetimes of photogenerated excited carriers, a detailed understanding about their origin and nature is required. In this report, we monitor the ultrafast charge carrier dynamics of CuInS2 (CIS), CuInSSe (CISSe), and CuInSe2 (CISe) nanocrystals, before and after ZnS shelling, using state-of-the-art time-resolved laser spectroscopy with broadband capabilities. The experimental results demonstrate the presence of both electron and hole trapping intra-bandgap states in the nanocrystals which can be removed significantly by ZnS shelling, and the carrier dynamics is slowed down. Another important observation remains the reduction of carrier lifetime in the presence of Se, and the shelling strategy is observed to be less effective at suppressing trap states. This study provides quantitative physical insights into the role of anion composition and shelling on the charge carrier dynamics in ternary CIS, CISSe, and CISe nanocrystals which are essential to improve their applicability for photovoltaics and optoelectronics.