We study in detail the properties of the stellar populations of 111 massive [log(M*/M_{sun}_) => 10] dusty [far-infrared (FIR)-selected] starburst (SFR/SFRMS > 2) galaxies at 0.7 < z < 1.2. For that purpose, we use self-consistent methods that analyse the UV-to-FIR broad-band observations in terms of the stellar light and dust re-emission with energy-balance techniques. We find that the emission of our starburst galaxies can be interpreted as a recent star formation episode superimposed on a more evolved stellar population. On average, the burst age is ~80 Myr and its attenuation ~2.4 mag. Assuming our starburst galaxies at half their lifetimes, we infer a duration of the starburst phase of ~160 Myr. The median stellar mass and star formation rate (SFR) are log (M*/M_{sun}_) ~ 10.6 and ~220 M_{sun}_/yr. Assuming this SFR and the inferred duration of the starburst phase, the stellar mass added during this phase corresponds to ~40 per cent the median stellar mass of our sample. The young-population age determines the position of our galaxies in the M*-SFR plane. Galaxies located at the largest distances of the MS present shorter young-population ages. The properties of the underlying stellar population cannot be constrained accurately with our broad-band data. We also discuss the impact of including the FIR data and energy-balance techniques in the analysis of the properties of the stellar populations in starburst galaxies.