Yes, that looks correct for everything except the white wire.

There should be a specific wire in your car that goes on when the dash lights get turned on. This is the headlight sense wire. If the wire you've connected is behaving as you're describing it (only goes +12 when the running lights are on, but does not go +12 when the headlights are on), then it's the wrong wire and you need to find the correct wire. That's why it's blowing your running light fuse.