Fine-tuning of the Cr3+ zero-phonon R1-line fluorescence (2E-4A2) has recently been achieved by varying the composition of Cr-doped solid solution garnets. Chemical substitutions of Y3+ with Lu3+ and Tb3+ produce R1-line shifts and multiplets that cannot be associated with direct or indirect changes in the Cr-O covalency alone and raise important questions on the nature of the interactions between the CrO6 active center and its environment, hence on the impact of local disorder. In this Letter we show that Pauli antisymmetry interactions with next-nearest neighbor ions, which are commonly omitted from theoretical analyses, induce a nephelauxetic effect on the CrO6 active center that shifts the R1-line. The strength of these interactions increases with the ionic radius and number of codopant ions, all of it resulting in controlled shifts and multiplets of R1-lines. The Pauli antisymmetry induced nephelauxetic effect, combined with the R1-line shift with lattice constant, allows for a very fine-tuning of the Cr3+ R1-line.