The study sounds like it is trying to blame the problem on the suffers (the "contagion" of their depression), but the obvious explanation of this is that by hiring from organizations with high stress, you're likely to be hiring perpetrators. That explains why it is not more likely to happen when the individual being hired is diagnosed ("Employees leaving unhealthy organizations act as “carriers” of these disorders regardless of whether they themselves have received a formal diagnosis"), and also why it is more likely to happen when they enter a position of power ("The effect is especially pronounced if the newcomer holds a managerial position.").
I am also not sure if the social contagion model has a lot of evidence for it. If you apply epidemiological models to any data you will get fits for epidemiological model parameters, and those will have a built-in epidemiological interpretation - but without prior knowledge that mental disorders are contagious (I thought most were definitely not?) you would just be making blind nonlinear curve fits to generic functions with many possible explanations.