We investigate whether the anomalous tensor operators with the Lorentz structure σ_μν(1 + γ₅) ⊗ σ^μν(1 + γ₅), which could provide a simple resolution to the polarization anomaly observed in B→φK* decays, could also provide a coherent resolution to the large B(B  ηK*) and survive bounds from B  ηK decays. Parameter spaces satisfying all these experimental data are obtained, and found to be dominated by the color-octet tensor operator contribution. Constraints for the equivalent solution with (1 + γ₅) ⊗ (1 + γ₅) operators are also derived and found to be dominated by the color-singlet one. With the constrained parameter spaces, we finally give predictions for B_s  φφ decay, which could be tested at the Fermilab Tevatron and the LHC-b experiments.