We study the effect of an exchange interaction on the magnetic-field-dependent photoluminescence in singlet fission materials. We show that, for strongly interacting triplet exciton pairs (intertriplet exchange interaction greater than the intratriplet spin-dipolar interaction), quantum beating and magnetic-field effects vanish apart from at specific magnetic fields where singlet and quintet levels are mixed by a level anticrossing. We characterize these effects and show that the absence of a magnetic-field effect or zero-field quantum beats does not necessarily mean that fission is inoperative. These results call for a reconsideration of the observations that are considered hallmarks of singlet fission and demonstrate how the spin coherence and exchange coupling of interacting triplet pairs can be measured through magneto-photoluminescence experiments.