Classical molecular dynamics simulations have been performed in polarizable and nonpolarizable force fields for series of electrolytes based on MeTFSI (Me = Li, Na) salts dissolved in EMIM-TFSI ionic liquid. Structure and dynamics of the solvation shell of me ions have been investigated. Contributions to the total conductivity of the electrolyte arising from motions of different ions and cross-correlations between them have been analyzed. The analysis has indicated that regardless of the type of Me+ cation, motions of Me+ ions and ionic liquid anions are positively correlated, contributing toward conductivity decrease and leading to negative transference numbers of metal ions. The results have confirmed experimental findings of negative transference numbers of Li+ and have suggested that the effect of Me-anion correlations certain concentration range is a general feature of Me+ solutions in ionic liquids.