If I remember correctly this isn't addressed in much depth in the article but this is what the author had to say about therapists' concerns re: effect of crying on clients:

"From the perspective of the therapists we surveyed, therapists felt that their tears had some important positive impacts on their clients -- 82% believed therapist crying led to the client feeling that the therapist genuinely cares about him/her, 72% that the client would feel the relationship was more authentic, and 61% that therapist tears would give the client permission to feel and express emotion. On the other hand, 69% of therapists expressed concern that therapist crying would cause the client to be concerned that the therapist would not be able to handle the client's emotion, 64% were worried that the client would feel burdened by the therapist's emotion and 56% thought that therapist tears could cause a role reversal in which the client would feel he/she would have to care for the therapist."

(Link to interview)