Is it considered a verbal resignation?

So, I got an offer from another company and I told my supervisor about that offer; however I'm still debating whether to take that or not.

My supervisor was upset and assumed that I will take the job right away but I told him I'm still considering it. I have't turned in my resignation letter, or even said yes to the other company; however my supervisor assumed that I will leave and sent out a resignation email to everyone who works under me, as well as submit my resignation paperwork to HR.

The company I'm currently working for is a public company; hence does verbal notice apply? My supervisor and I never had any discussion about when my last day is and I haven't submitted my resignation letter. My supervisor is so emotional about it, and I'm so mad because I first decided to stay and help for the time being; but I feel that I'm being kicked out.