The constitutional conflict in this case was that the wording of the exemption wasn't open to all religions without interpretation. Instead of allowing that to be a barrier, the judge (and the JW lawyer agreed) decided to apply JW practice to the wording.
States can individually decide whether or not to allow an exemption. eg West Virgina and New Hampshire specify they do not recognise a clergy privilege in these cases and require clergy to report, as does Guam. Four other states (including Texas) don't mention clergy specifically but do say there is no clergy penitent privilege when it comes to reporting child abuse. source: https://www.childwelfare.gov/pubPDFs/clergymandated.pdf
So the issue is whether JWs fit the exemption as worded in Delaware. If they don't, they report as they have to do in other states already. If they do, they get an exemption in Delaware as they have in other states already.
The lack of an exemption in other states hasn't changed how they operate a JC. I presume, however, they do report in those states - as they are legally required. The question is whether or not the Delaware case will undermine their claim to clergy/penitent privilege in those states where they claim it. I suspect that much will depend on the wording of legislation and the willingness of people to press a prosecution.
eg Illinois' definition of this privilege seems impossible to challenge on the same grounds as that of Delaware.
A member of the clergy or practitioner of any religious denomination accredited by the religious body to which he or she belongs
shall not be compelled to disclose in any court, or to any administrative body or agency, or to any public officer, a confession or
admission made to him or her in his or her professional character or as a spiritual advisor in the course of the discipline enjoined by
the rules or practice of such religious body or of the religion that he or she professes, nor be compelled to divulge any information
that has been obtained by him or her in such professional character or such spiritual advisor.