Through straight synchronization and proper manipulation of a sequential Monte Carlo glass-forming rule introduced by Fröbose and Jäckle [J. Stat. Phys. 42, 551 (1986)], we constructed a synchronous, non-glass-forming rule for diffusion of mutually exclusive particles in a lattice of adsorption sites. The rule satisfies detailed balance in the presence of both homogeneous and heterogeneous adsorption energies. Our model differs from the usual lattice-gas cellular automata diffusion rules in that the mutual exclusion holds on the lattice sites rather than on the channels which connect neighboring sites, and from the mass-conserving cellular automata rules in the use of a no-partitioning scheme. The first aim of this work is to show that, although some prescriptions in the synchronous rule are introduced just to allow that both detailed balance and mutual exclusion can coexist with synchronicity, the diffusion process produced by the rule is not anomalous so that the rule can be regarded as a diffusion model. We then compare the diffusion isotherms of several test systems with the ones obtained by means of sequential Monte Carlo simulations of Arrhenius jumps of particles on a lattice. Finally, we apply the rule to the case of a (100) fcc model surface and estimate the amount of time correlation in the migration process, and show that the synchronous rule produces higher correlations and slightly lower diffusivity than the sequential Monte Carlo counterpart.