From their website:
"If the school requires cancelling the contract in advance unreasonably, Chinaicec will offer another position for the foreign teacher in a short time. During this period, Chinaicec will be in charge of the teacher’s fees including the salary. However, if the foreign teacher is not satisfied with the school, he or she has to inform Chinaicec before one month and then Chinaicec will arrange another school for the teacher one month later."

This type of "agency" is not facilitating your employment at a qualified school. They are shopping you around, keeping you a few steps ahead of the police. Legitimate employment in China is ONE visa attached to ONE qualified school. Legitimate recruiters can legally locate those jobs for you and receive a fee from the school. Agencies that bounce you among employers, providing you with an agency salary, are operating illegally.