Caesium titanium alum, CsTi(SO4)(2) . 12H(2)O, is a beta alum and exhibits a large trigonal field and a dynamic Jahn-Teller effect. Exact calculations of the linear (2)T(2)xe Jahn-Teller coupling show that in the strict S-6 Site symmetry the ground multiplet consists of a Kramers doublet 2 Gamma(6) with magnetic splitting factors g(parallel to)=1.1 and g perpendicular to=0, a Gamma(4) Gamma(5) doublet at similar to 60 cm(-1) with g(parallel to)=2.51 and g(perpendicular to)=0.06 and another Gamma(4) Gamma(5) doublet at similar to 270 cm(-1) with g(parallel to)=1.67 and g(perpendicular to)=1.83. The controversial g values observed below 4.2 K, g(parallel to)=1.25 and g(perpendicular to)=1.14, are shown to arise from low symmetry distortions. These distortions couple the vibronic levels and induce into the ground state the off-diagonal axial Zeeman interaction that exists between the first excited and the ground vibronic levels.