By developing models of increasing complexity, we show that a model without single-ion anisotropy (SIA) cannot explain the magnetic properties of Jeff=1/2 Tb3+ moments in the orthorhombically distorted, honeycomb material Tb2Ir3Ga9. In four different models for the magnetization of a single honeycomb layer, the only sources of anisotropy are symmetric exchange interactions Jnαβ=Jnβα along three different bonds n, an anisotropic g– tensor, and a Dzyalloshinskii-Moriya interaction (asymmetric exchange) that produces the observed canted moment along b. With 21 parameters, the best such model yields χ2=0.065, which is substantially smaller than χ2=0.112 obtained using a Heisenberg model containing six parameters including easy-axis anisotropy. However, models without SIA fail to reproduce the linear dependence of the magnetization with a field perpendicular to the Ising axis while predicting a saturation magnetization that is far too low. Due to the complex crystal-field environments, we argue that SIA is necessary to study low-symmetry, three-dimensional Jeff=1/2 materials containing Tb3+ ions.