  A violation of the distance-duality relation is directly linked with a
temporal variation of the electromagnetic fine-structure constant. We consider
a number of well-studied $f(T)$ gravity models and we revise the theoretical
prediction of their corresponding induced violation of the distance-duality
relationship. We further extract constraints on the involved model parameters
through fine-structure constant variation data, alongside with supernovae data,
and Hubble parameter measurements. Moreover, we constrain the evolution of the
effective $f(T)$ gravitational constant. Finally, we compare with revised
constraints on the phenomenological parametrisations of the violation of the
equivalence principle in the electromagnetic sector.
