Well, that’s more or less I meant about the unidentifiable parameters. Basically, in the linear model mu = tt.exp(b0 + mu_phi + tt.log(offset)), if the mu_phi is not centered on zeros, the intercept is basically distributed to b0 and the mean of mu_phi. But if you centred mu_phi as in the original code, the trace of mu_phi is not interpretable anymore, as all the the mu_phi can move around up and down together; what matter is the phi.
Both case it doesnt change your model prediction, as when you combine the linear model mu = tt.exp(b0 + mu_phi + tt.log(offset)) they will be the same. To have more identifiable you should reparameterized your model.