We present a theoretical study of synchronisation dynamics of incoherently pumped exciton–polariton condensates in coupled polariton traps. Our analysis is based on a coupled-mode theory for the generalised Gross–Pitaevskii equation, which employs an expansion in non-Hermitian, pump-dependent modes appropriate for the pumped geometry. We find that polariton–polariton and reservoir-polariton interactions play competing roles and lead to qualitatively different synchronised phases of the coupled polariton modes as pumping power is increased. Crucially, these interactions can also act against each other to hinder synchronisation. We map out a phase diagram and discuss the general characteristics of these phases using a generalised Adler equation.