For Michelle Zhao, a Shanghai resident, offshore trusts had long appeared to be the preserve of people far wealthier than herself. That assumption was upended two weeks ago when she received a “baffling” text message from the Hongkou district branch of the Shanghai Municipal Tax Service.“The message said I might have taxable gains stemming from offshore trusts that I was required to declare. Yet I have never held any form of trust. I assumed the message was sent to me by mistake, so I ignored...