Mavericks now considers each monitor a “Space”. As a result, apps launch and have their menu bar in whichever monitor they were launched from. However, it’s easy to assign apps to each monitor. Here’s how:

First, you need to create an additional space in Mission Control. You can add it to either monitor.

Having done that, then when you right-click on an app in the Dock, you will see the option to assign the app to All Desktops, Desktop on Display 1, Desktop on Display 2.

Source: Mac OSX Hints