I'm pretty sure the game just gave me 10 gold while I was logged off, and I lost it all to other players. I emptied my pockets before logging off, so unless it gave it to me as I was clicking the log off button, it gave it to me while I had no chance to protect it. That being the case, the reward caused me more harm than good by lowering my gold won in duels stat. The game shouldn't hand out gold while you're offline. Tax collector and cutpurse already provide a flow of offline gold for attackers to loot, so it's not like it would stifle dueling or something to let you have a chance at your reward gold. On the bright side, I took most of it back from both players, each of whom is a higher level than I am, and both of whom were online at the time. #plunderedbutnotpunked
The achievement code should only get processed when you do a page load with your character. Specifically, the page load AFTER your action to earn that achievement. I don't think Logout counts towards that, but I can double check. I haven't noticed that happening, but I don't log out my characters very often as I mainly just run them in different browsers.