Avoid adding exception on website if ca-certificate is not installed - ssl

Question

I have created my own ca certificates with openssl. I have four files :
ca.key (private ca key)
ca.crt (public ca certificate)
server.key (private key)
server.crt (public certificate signed by the ca files)
I use nginx with ssl configuration.
ssl_certificate server.crt;
ssl_certificate_key server.key;
If I install the ca public certificate on my computer, my browser let me go on the website without adding exception which is good. But if I have not the ca certificate installed on my computer, I have to add exception to pass. I want to avoid adding exception and force user to have the ca certificate installed on their computer.
I configure nginx with hsts (http strict transport security) :
add_header Strict-Transport-Security "max-age=31536000; includeSubDomains" always;
ssl_stapling on;
ssl_stapling_verify on;
ssl_trusted_certificate ca.crt;
Unfortunately I have again the possibility to add an exception to pass.
I'm wondering if it is possible to do this ?

Answer 1

I realize that my certificates doesn't work with chrome missing_subjectAltName. So I fixed it with this link. And now I have this message with chrome if my ca certificate is not installed on my computer :
You cannot visit localhost right now because the website uses HSTS. Network errors and attacks are usually temporary, so this page will probably work later.
This is exactly what I want. However it doesn't work on firefox et let me the possibility to add an exception.
Why chrome block it and not firefox ? How can I do that on firefox too ?