It is a simple matter to find out. Ask the employer for the legal basis for this “requirement”.
After all, if it is not specified in the law, the employees could refuse to respect such an agreement, and if the employer ever tried to sue them for the money, he would lose.
I ran into a similar situation when I was working in a bushiban many years ago. The Bureau of Labor Insurance called and said that we had too many people coming and going, i.e. being processed in and then being processed out.
I asked the lady: “What law have we violated?”
She said that there was no specific law about it. I said: “Then what is the problem? If you want us to say that people who sign up for Labor Insurance through one employer must remain signed up through that employer for a minimum of six months, or one year, then fine. Tell me which Article of the relevant law specifies that requirement and we will revise our company rules immediately.”
She said that there was no such legal requirement. I said: “Well, then, I think you should wait until such a revision is passed to the law and call me up then. Now you seem to be complaining that there are too many people in our company being processed in and processed out for Labor Insurance, all within a short amount of time. Yet there is clearly no legal basis for your complaint.”
She gave up at that point and said goodbye.
I think that a similar analysis applies to the above situation regarding monthly fees for NHI. If it is not specified in the law, then you have no basis for demanding that employees comply with such a requirement, even if they sign the contract.