First, we need to assume that the minimum wage is an "effective constraint", i.e. that in the cases examined people are paid the minimum wage. I guess this holds.
Second, the negative relation between demand for labor (for the services sold by workers) and wage (its price), depends on an assumption of a smooth such relation. In turn, such a smooth relation depends on substitutability of factors of production: in order to decrease labor employed, one needs to increase capital employed (if it has no reason to alter the production level).
Is it the case that the services offered by minimum wage workers in the study mentioned, could be readily substituted by capital? If not, here is one explanation.
Another way for a firm to respond to a minimum wage increase, is to try to increase the intensity of work, so it could fire people and maintain essentially the same level of services with fewer workers that are paid the higher minimum wage, keeping the total cost the same.
Is it the case that minimum wage workers in the study mentioned worked with some slack, and there was still room to press them to work harder? If not, here is another explanation.
So it may be the case, that the firms have done their "profit making job excellently", and have managed to have the lowest operationally possible level of labor, by extracting full efficiency from it, but also from the point of view of factors substitution capabilities... and then came the minimum wage increase. The firms simply had no options, (at least in the short run), than, perhaps, to pass the cost over to consumers, or live with lower profits, because they were already operating at their efficiency frontier with the minimum feasible amount of labor.
In such a case, the minimum-wage increase has a pure income-redistribution effect.