First off, I do not have an Antuino (yet, waiting for availability after June 1), however have done some research into barrel connectors and I am pretty sure there is an error in the schematics provided on GitHub.
Here is the barrel connector provided (deduced from the pictures):

As you can see, the battery negative needs to be connected to pin 3 so that it is removed from the power supply when the power supply is connected through the barrel connector.? This would agree with what WoodJRx explained in message #69028.? This also aligns with the one comment from Ashhar on needing to insure proper soldering of pin 3 of this connector.
Ashhar needs to update the schematics, or else use a different part for the barrel connector (there are version that switch the pin connection)..
Above are my observations, and may be in error.? Use at your own risk!
73
Evan
AC9TU