You are told to enter on a business or tourist visa and start teaching while the work permit is 'being sorted'. Working in a school on that visa is not legal. It leaves you with no labour protections, and it is the teacher who carries the risk.
A Z visa and a work permit should exist before you start teaching. If you are asked to begin on anything else, treat it as a hard stop.
Same first-person account as the probation case above.