Alex Cooper's husband has a reputation for berating and yelling at staffers working at Alex's Unwell Network, even bringing one of them to tears ... at least according to a new report.

Matt Kaplan reportedly oversees day-to-day operations at Unwell in his role as CEO ... and according to Bloomberg, his alleged outbursts have led crew to threaten to quit on the spot during filming and live tours.

In one alleged incident, Matt brought a staffer to tears when he "berated the staff on set and threatened to prevent them from ever working in Hollywood again if they messed up." Crew members allegedly filed formal complaints threatening to quit if Matt didn't clean up his act.

The report says there's a lot of staff turnover at Unwell Network ... with the company's head of brand marketing, head of the network, and chief growth officer leaving in the past year.

Meanwhile, Alex is feuding with Alix Earle ... so it sounds like there's a lot of drama in her world.