In this work, we studied the phase transitions and exchange bias of Ni50−xMn36Sn14Tx (T = Pd, Pt; x = 0, 1, 2, 3) alloys. An intermartensitic transition (IMT), not observed in Ni50Mn36Sn14 alloy, was induced by the proper application of negative chemical pressure by Pd(Pt) doping in Ni50−xMn36Sn14Tx (T = Pd, Pt) alloys. IMT weakened and was suppressed with the increase of applied field; it also disappeared with further increase of Pd(Pt) content (x = 3 for Pd and x = 2 for Pt). Another striking result is that exchange bias effect, ascribed to the percolating ferromagnetic domains coexisting with spin glass phase, is notably enhanced by nonmagnetic Pd(Pt) addition. The increase of unidirectional anisotropy by the addition of Pd(Pt) impurities with strong spin-orbit coupling was explained by Dzyaloshinsky-Moriya interactions in spin glass phase.