It might be better to make it public. Set an example, that such behavior will not be tolerated in a modern democracy.
If a handful of the most vocal professors, that are supporting terrorism and inciting violence with their students, are fired and even criminally charged, it will send a message to all the others.
And mind you, there is a paradox in the democratic system, that dictators and extremists try to use to sabotage it.
The idea is that in a democracy, that all forms of speech are to be allowed. And because of that, instigators, can use that same preset to attack democratic institutions.
But the reality, is that democracy has to defend itself against authorities and extremism.
Also consider that in a free society, inciting others to do violence is a crime, no matter the reason.
So a professor that is inciting students to attack other students and professors, and that are supporting terrorist organizations, are committing a crime.