Temperature dependences of the CW-EPR spectrum as well as the electron spin-lattice relaxation time T-1 and phase memory time T-M determined by electron spin echo were measured for Cu(2+) ions in (NH4)(2)Mg(SO4)(2) . 6H(2)O Single crystal. The dependences are dominated by vibronic behavior of the Cu(H2O)(6)(2+) complex and connected to the dynamic Jahn-Teller effect producing reorientations between two lowest energy wells of the adiabatic potential surface. Below 70 K the static Jahn-Teller effect is observed, and the system is strongly localized, by the local strains, in the deepest potential well leaving higher wells not populated. Above this temperature the second well becomes progressively populated, and a rapid averaging of the g(z) and g(y) factors as well as corresponding hyperfine splittings appears. The Boltzmann population of these two wells is achieved at 160 K. Simultaneously with g factors averaging a continuous broadening of the hyperfine lines is observed with line shape transformed from Gaussian at 70 K to Lorentzian at 160 K. The averaging and broadening processes are thermally activated with energy barrier delta(12) = 108 +/- 3 cm(-1) = 156 K = 1.26 kJ/mol being the energy difference between the two deepest potential wells. Electron spin relaxation was measured below 50 K where electron spin-echo signal was detectable. Spin-lattice relaxation is driven by the direct and Raman processes with relaxation rate 1/T-1 = aT + bT(5) as expected for dynamic Jahn-Teller systems. Spin-spin phase relaxation described by the phase memory time T-M depends on temperature as 1/T-M = a + bT + c exp(-Delta lkT) with Delta = 102 +/- 2 cm(-1) At low temperatures the higher energy well is not populated; thus, a can be assigned as the energy of the first excited vibronic level in the deepest well. The Delta and delta(12) are temperature-independent, indicating that adiabatic potential surface is not affected by temperature. We suggest that the deviations of experimental data from theoretically predicted vibronic g-factors averaging observed for Cu2+ in many Tutton salt type crystals are not due to temperature variations of the local strains or barrier height but are due to the fact that Boltzmann population of the potential wells cannot exist at low temperatures. This effect is especially pronounced for Cu2+ ions in (NH4)(2)Mg(SO4)(2) . 6H(2)O since the energy Delta of the first vibronic level is lower than the energy difference delta(12), between adjacent wells. In such case the phonon-assisted tunneling jumps between the energy wells induced by two-phonon Raman processes via virtual state of energy delta(12) become to be effective when kT greater than or equal to delta(12)/2, and the Boltzmann population of the second well is achieved via direct phonon process when thermal phonons of energy kT greater than or equal to delta(12) are available.