All checking is done locally on your machine from a hashed list of "bad" domains, your visits aren't sent to google. You can get the full details here: https://support.mozilla.org/en-US/kb/how-does-phishing-and-malware-protection-work

This is a protection mechanism to prevent laymen from falling for scam websites. It is a service offered by Google, enabled by default in Firefox. It can disabled in the configs.

Are they submitting that to Google or are they subscribing to some hashed list google has of domains with (according to them) know malware, issues, etc?

In that case everything happens on your pc and doesn’t go to google or Mozilla