Numeration systems are maps between a set of numbers and a set of words that act as representations of these numbers. One desirable property is positionality: the ability to relate positions in the words to values of the numbers. In general, positionality is hard to decide. In this article, we obtain a criterion to decide the positionality of so-called Dumont–Thomas numeration systems, arising from substitutions. Then, we particularize this criterion to some well-behaved classes of substitutions, allowing us to link the related systems to existing literature.