SSO is applied to Office 365?

SSO can mean a few things when it comes to O365 though, from AAD SSO to AD FS to AAD Join and more. All of them require deliberate action on admin and/or user's part though, it will not just "start working" on its own. This includes configuring browsers to properly support it, where applicable. But since you are a bit vague on the details, we can only guess which method you have actually configured and whether you need help with it :)

I had it working on chrome at my last org. It is a supported scenario as listed here: https://docs.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-sso