Accommodating digital twins (DTs) in the metaverse is essential to achieving digital reality. This need for integrating DTs into the metaverse while operating them at the network edge has increased the demand for a decentralized edge-enabled metaverse. Hence, to consolidate the fusion between real and digital entities, it is necessary to harmonize the interoperability between DTs and the metaverse at the edge. In this paper, a novel decentralized metaverse framework that incorporates DT operations at the wireless edge is presented. In particular, a system of autonomous physical twins (PTs) operating in a massively-sensed zone is replicated as cyber twins (CTs) at the mobile edge computing (MEC) servers. To render the CTs' digital environment, this zone is partitioned and teleported as distributed sub-metaverses to the MEC servers. To guarantee seamless synchronization of the sub-metaverses and their associated CTs with the dynamics of the real world and PTs, respectively, this joint synchronization problem is posed as an optimization problem whose goal is to minimize the average sub-synchronization time between the real and digital worlds, while meeting the DT synchronization intensity requirements. To solve this problem, a novel iterative algorithm for joint sub-metaverse and DT association at the MEC servers is proposed. This algorithm exploits the rigorous framework of optimal transport theory so as to efficiently distribute the sub-metaverses and DTs, while considering the computing and communication resource allocations. Simulation results show that the proposed solution can orchestrate the interplay between DTs and sub-metaverses to achieve a 25.75 % reduction in the sub-synchronization time in comparison to the signal-to-noise ratio-based association scheme.