Context. Periodic flares of maser emission are thought to be induced either by variations of the seed photon flux in young binary systems or the pump rate regulated by stellar and accretion luminosities. Aims. We seek to study the variability of four maser transitions of three different species in G107.298+5.639 to constrain the dominant mechanism of periodic flares. Methods. Light curves of the 6.7 GHz methanol and 22.2 GHz water vapour maser were obtained with the Torun 32 m radio telescope over 39 and 34 cycles, respectively. The target was also monitored at the 1.6 GHz hydroxyl transitions with the Nançay radio telescope over 13 cycles. All these maser lines were imaged using VLBI arrays. Results. The study confirms alternating flares of the methanol and water masers with a period of 34.4 d and reveals the synchronised behaviour of the methanol and hydroxyl masers in this source. The observed spatial distribution of the methanol maser cloudlets and the measured time delays of the flares of individual features imply a ring-like structure of radius 240 au and thickness 30 au. Internal proper motions indicate that the velocity of methanol cloudlets is dominated by a disc-wind component of about 5 km s −1 . The methanol emission detected during only one VLBI observation is located in a region about 550 au from a central star, which also exhibits OH maser flares. The erratic appearance of methanol features can be related to a powering object of relatively low luminosity which, during some variability cycles, can excite molecules only in the nearest part of the disc. A careful analysis of the maser and infrared light curves reveal a strong correlation between the 6.7 GHz line and the infrared flux densities supporting a radiative pumping of the maser. Conclusions. The synchronised behaviour of the hydroxyl 1665/1667 MHz and 6.7 GHz methanol transitions indicates a common pumping mechanism for the periodic flares of G107.298+5.639.