Would I have a case to sue someone for notifying Fb about my using another's trademark for my business if it on the supplemental register?
Patent Infringement Attorney
This is not to be construed as legal advice, and I am not your attorney, A conflict check and engagement letter would necessarily be required before any retention or attorney/client privilege exists.
Intellectual Property Law Attorney
NO. That "someone" has a right to assert a registered trademark by notifying Facebook of the registration and your use of it, even if just a supplemental registration. It is unclear if "someone" and "another" are the same person. That's the problem with use of pronouns, as pronouns [especially "it" and "they", although here "another" and "someone" result in similar ambiguity] can lead to ambiguity. Registered patent attorneys are often trained to strictly avoid use of pronouns to avoid ambiguity.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Patent Application Attorney
Can you sue someone for notifying the police about a crime? No. You cannot have a cause of action against a third party witness unless the testimony or accusation is blatantly false or malicious.