We describe a numerical method that simulates the interaction of the helium atom with sequences of femtosecond and attosecond light pulses. The method, which is based on the close-coupling expansion of the electronic configuration space in a B-spline bipolar spherical harmonic basis, can accurately reproduce the excitation and single ionization of the atom, within the electrostatic approximation. The time-dependent Schrödinger equation is integrated with a sequence of second-order split-exponential unitary propagators. The asymptotic channel-, energy-, and angularly resolved photoelectron distributions are computed by projecting the wave packet at the end of the simulation on the multichannel scattering states of the atom, which are separately computed within the same close-coupling basis. This method is applied to simulate the pump-probe ionization of helium in the vicinity of the 2s/2p excitation threshold of the He+ ion. This work confirms the qualitative conclusions of one of our earliest publications [Argenti and Lindroth, Phys. Rev. Lett. 105, 053002 (2010)], in which we demonstrated the control of the 2s/2p ionization branching ratio. Here we take those calculations to convergence and show how correlation brings the periodic modulation of the branching ratios in almost phase opposition. The residual total ionization probability to the 2s+2p channels is dominated by the beating between the sp+2,3 and the sp+2,4 doubly excited states, which is consistent with the modulation of the complementary signal in the 1s channel, measured in 2010 by Chang and coworkers [Gilbertson et al., Phys. Rev. Lett. 105, 263003 (2010)].