Music-making relies on precise temporal control and mutual coordination among performers, particularly to maintain tempo. We evaluate the impact of human-machine interaction and rhythmic subdivisions on tempo change in musical trios. A synchronization-continuation task was performed by trios of human participants interacting with confederates or with algorithmic (i.e. machine) models. Sounded tone onsets were produced by a linear error-correction model, delay-coupled model, and Kuramoto model that replaced a human participant. Inter-onset intervals were examined from participants who performed rhythms in both in-phase and anti-phase conditions while a third group member was either a human or algorithmic model. Trios drifted toward faster tempi more when they contained a human than an algorithmic model. Tempo drift also increased for the aligned rhythms (in-phase) compared to rhythms with rhythmic subdivisions (anti-phase). Finally, the tested algorithmic models replicated the confederate's tempo drift without the use of any period correction mechanisms. This research advances our understanding of unintentional tempo drift, offering insights into ensemble dynamics and models of temporal coordination in groups. Implications for musical coordination and avenues for future research are discussed.