We analyze the Belle data [K. F. Chen (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008); I. Adachi (Belle Collaboration), arXiv:0808.2445] on the processes e+ e- --> Upsilon(1S)pi+ pi-, Upsilon(2S)pi+ pi- near the peak of the Upsilon(5S) resonance, which are found to be anomalously large in rates compared to similar dipion transitions between the lower Upsilon resonances. Assuming these final states arise from the production and decays of the J(PC)=1(--) state Y(b)(10,890), which we interpret as a bound (diquark-antidiquark) tetraquark state [bq][bq], a dynamical model for the decays Y(b) --> Upsilon(1S)pi+ pi-, Upsilon(2S)pi+ pi- is presented. Depending on the phase space, these decays receive significant contributions from the scalar 0(++) states, f0(600) and f0(980), and from the 2(++) qq-meson f(2)(1270). Our model provides excellent fits for the decay distributions, supporting Y(b) as a tetraquark state.