We discuss the critical behaviour of the q-state Potts model on a diamond-like hierarchical lattice with ferromagnetic interactions according to an aperiodic two-letter substitutional sequence. We show that the geometric (deterministic) fluctuations become relevant for , where is the wandering exponent of the sequence, D is the fractal dimension of the lattice, and is the critical exponent associated with the specific heat of the uniform model. We also point out that the criteria for analysing the relevance of deterministic and random fluctuations are generically different.