Our local RSM said that students had to take a placement test to determine their grade placement - for e.g., if your child is now attending 3rd grade at their day school, but passed RSM's 5th grade level assessment, then he will be placed in the 6th grade RSM class and within that 6th grade RSM class, an appropriate sub-level will be assigned. They also said that there is some flexibility in the placement if the class turns out to be too difficult or too easy for the student. So, to answer the OP's question, placement is based on the child's ability and knowledge rather than age and grade level at school.
Our local center seems to have a mastery based approach using Russian methods. I believe that they also introduce critical thinking and problem solving in math. They had not heard of AOPS when I called them. I decided to go with AOPS instead.
