What your client says would be applicable if the salary is increased after the first contribution is already made in that contribution period. Since you confirmed that the salary was greater than 15000 in the original April payroll, this means that the employee is not eligible for ESIC during the contribution period (Apr-Sept) and not a single contribution is made. Can you reconfirm your client's requirement and ask them to substantiate it with a circular number?
The only way your client's requirement can be justified is if April payroll was run where the salary<15000 so the ESIC contribution was made, after which, in some subsequent month, the salary was increased effective April.