I’m pretty sure that priests are not canonically required to instruct penitents to turn themselves in. In fact I think it’s almost the opposite. The priest is not allowed to “force” a penitent to do anything that would damage the penitent’s reputation.
For instance if the sin was theft the priest could require the penitent to give what was stolen to the priest who would then return it, unless even that would give away the person’s identity and then the ill gotten goods would be given to charity or some other solution arranged so long as the thief didn’t profit from his crime.
Beyond all that we’re talking about child abuse here and as far as I understand, most of these “people” (and I use the term loosely) don’t think they’re doing anything wrong anyhow.
I followed up with an actual priest, he confirmed what I believed to be the case. Confessors can “encourage” penitents to turn themselves in but they can’t make it a condition of absolution. Absolution can only be withheld if the “penitent” shows a positive lack of contrition.
Furthermore he went on to say that “it’s not the abusers who come to confession with this stuff, it’s the victims and the victims are expressly expecting the priest to keep his mouth shut”. That at least has been his experience. I thanked him for confirming once again that the priesthood was not my vocation.
By that I mean: a priest always has the duty to withhold absolution if he is convinced that the penitent is not in fact repentant, does not acknowledge the seriousness of his sin, or shows no purpose of amendment. To do otherwise would be to participate in a fraudulent confession, i.e. sacrilege.
Undertaking corrective actions like reporting to civil authorities can be part of the confessor's instructions to the penitent as a matter of justice --- especially if it will save some innocent person from becoming a suspect or being unjustly accused --- and in fact the penitent can ALWAYS reveal what was said in the Confessional (the penitent is not bound by the seal).
But OTOH it cannot be imposed as a "condition" for absolution because:
If a penitent were to say, "Remember what we were talking about last week?" the priest would have to say, "Whether I remember or not, I am required by the seal to leave it there. That slate is clean. So you need to tell me about it as if I've never heard it before."
A priest can't force things in any case. (There's no enforcement mechanism. He's not with the Mafia!) So the best he can do if the guy has clearly not shown the requisite desire and intention of amendment, is refuse absolution.