Though there were fears that the update might fix the bugs used by the recently released iOS 6.x evasi0n jailbreak, the evad3rs team has confirmed with a tweet (via iPhoneHacks) that the evasi0n jailbreak works with iOS 6.1.2 on an iPhone 5 and an iPad mini. Testing for other devices is still ongoing.
According to evad3rs team member @planetbeing, evasi0n 1.4 will be released later today with official support for iOS 6.1.2. The new update will allow jailbreakers to update to iOS 6.1.2. When released, the download will be available from the evasi0n website.
Update: Evasi0n 1.4 is now available for download.