While the children were calling the police,the old man -----

while引导时间状语从句有两种情况：
1、从句的动作进行的过程中,主句动作发生.
While I was waiting for the bus,I ran across an old friend.(我在等公交车时,偶遇老朋友)
2、主句动作和从句动作同时发生或进行.
While I was reading,my brother was watching TV.(我在看书,我弟弟在看电视)
你的问题应该是第二种情况：孩子们在报警时,老人在理发.不能说：孩子们报警时,老人开始理发.所以答案是正确的.而你的看法是错的.