It's normal procedure. No need to panic unless your stay in China is nearing 30 days. The poster 'Turino' knows what he's on about. If your school has already gone to the trouble of obtaining a letter of invitation for you, which was subsequently approved by the provincial authority, and with which you got your Z visa, you needn't worry. They're not about to dispense with you unless your teaching is well below average.
But if you're teaching with an L or an F visa, you could be vulnerable - as far as I know, you can no longer replace either by a Z in HK. That would make you highly dependent on your employer's 'special relationship', which probably wouldn't continue to be used to benefit you should your teaching disappoint him at any time. What's more, your contract isn't worth the paper it's written on. Even worse, if you are found out to be teaching illegally by the immigration department, you will be fined 5000 Yuan and given 10 days to leave the country; he'll be fined a great deal more for having employed you, and will maybe lose his right to employ foreign teachers.