For a non-Chrome web browser like Firefox to display an "urgent pop-up warning" about a Chrome browser update, the mechanism creating that message has to exist in: the system, its scheduler, or a specific malicious website (or an ad it's hosting). If the message is being triggered by your system or its scheduler, it indicates at least a system-account-level penetration by malware. If the message is triggered by a visiting a particular website, then you're dealing with a corrupt website or a malicious ad which the site is hosting.
You haven't linked the pop-up to a particular website URL in your posts, leading to a suspicion there is malware on your system. Is the pop-up occurring at multiple sites or at just one URL (in which case, which one? -- and please obfuscate any URL spelling of that site as noted earlier)?