Cellular automata are widely used to model natural systems. Classically they are run with perfect synchrony, {\em i.e.}, the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a discontinuity in the behaviour of the cellular automaton. This works aims at investigating the nature of this change of behaviour using intensive numerical simulations. We apply a two-step protocol to show that the phenomenon is a phase transition whose critical exponents are in good agreement with the predicted values of directed percolation.