personally, I wouldn't expect the allowance.
I work in three schools. the partnership was contracted amongst the schools before they adverstized for my position. I was offered a position and signed a contract that says I work in three schools.
I took on an afterschool activity class with a local high school. My contract says this is illegal and it actually prohibits it. My KT was pushing for me to take the position though and got permission from my principal to work the extra hours. I thought it was illegal in Korea for me to take the job, but its not korean law, just my contract. On the advice of a lawyer, I got the school to provide a written letter giving me permission to work the extra job.
but I sincerely doubt that we can make the schedule that we want to make and then start asking for multiple school allowances. also, my high school paid me by the month. I wouldn't wait until the end of term for salary. when I signed the contract, I knew that I would be paid once a month around the 3rd. hope that helps!