Angle-resolved photoemission spectroscopy (ARPES) reveals effects of electron doping, which is realized by Co and Ni substitution for Fe in FeTe$_{1-y}$Se$_{y}$ (y$sim$0.35) superconductor. The data show consistent band shifts as well as expansion and shrinking of electron and hole Fermi surface, respectively. Doping of either element leads to a Lifshitz transition realized as a removal of one or two hole pockets. This explains qualitatively a complex behavior of Hall coefficient observed before [Bezusyy, et al., Phys. Rev. B 91, 100502 (2015)], including change of sign with doping, which takes place only below room temperature. Assuming that Ni substitution should deliver twice more electrons to the valence band than Co, it appears that such transfer is slightly more effective in the case of Co. Therefore, charge doping cannot account for much stronger effect of Ni on superconducting and transport properties [Bezusyy, et al., Phys. Rev. B 91, 100502 (2015)]. Although overall band shifts are roughly proportional to the amount of dopant, clear deviations from a rigid band shift scenario are found. The shape of electron pockets becomes elliptical only for Ni doping, effective mass of electron bands increases with doping, strong reduction of effective mass is observed for one of hole bands of the undoped system. The topology of hole and electron pockets for superconducting Fe$_{1.01}$Te$_{0.67}$Se$_{0.33}$ with T$_{c}$=13.6 K indicates a deviation from nesting. Co and Ni doping causes further departure from nesting, which accompanies the reduction of critical temperature.
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