This is my first game jam; so I was wondering this. 
Normally when people install a demo I've made in Unity, the file gives a false warning about unknown publisher (I know that normally when publishing to Steam, they will handle that part). 

But this is my first time using itch.io, and thought I'd quickly make sure how this works in good time, before the submission deadline gets too close.

-So to be more specific about my question:

Will I have a problem with fake "potential virus"/"unknown publisher" showing up when publishing to itch.io?

My opinion: You might! People will run your game at their own risk, so some might not rate your game at all if they have to run it locally. Best advice is to create a web build and post it on itch.