To be honest, the prosecutors from the Busan District Prosecutors' Office's Special Investigation Division were acting quite meticulously back then..

To be honest, there was a reason why all those police officers were fired back in 2014 and 2015. The truth is, their identities were exposed far too much. At that time, the investigations were primarily led by inspectors who were high school graduates.
Furthermore, the identities of most members of the Busan Metropolitan Police Agency's Wide-area Investigation Unit, who were known for being good at investigating back then, were also exposed. So, they must have agonized over how to handle this.
However, around mid-October 2015, the Busan District Prosecutors' Office must have stepped in. At that time, prosecutors from the Special Investigation Division would have been deployed in full force.
Even when the child developed a mental illness in January 2016, it was likely at this point that the Busan District Prosecutors' Office confirmed which individuals could be identified and which could not.
So, they had someone follow them based on that.
Even though everyone else said there was no one there, this person kept noticing them.