Yes, I just found that out the hard way. Looking through my quests, the one that mentioned anything remotely financial was the one in Den of Danger. So I just went in and did that one. The Vampire boss at the end said something about giving me his services if I defeated both of his Economists in a combat trial. I've no idea what that means.
However, I finished the entire dungeon, racking up 182 gold, and then the quest rewarded me another 100. ALL this gold was completely lost, apparently. My bank remained at 474, because it was red, I guess, as you said. The elf race was unlocked, though, so I spent 200 upgrading their building so I can use them now.
So now my bank is 274, and not red. However, I've still got no idea how to upgrade the bank.
The puzzles are also unlocked, and doing all of the first set rewards 300. But that will not fit in the bank.
Another quest unlocked-- Beginner's Brigade, but that one rewards 1000 gold.
None of these are worth doing because the rewards won't fit in my bank.
Venture Capital is the other one open, which rewards 100, which will fit, so I guess I will do that next, and perhaps that is what the vampire meant? The other economist boss to beat is in there?
I am really liking the game, but this part of it is not fun at all. The game tells me to do the Lord Gobb easy dungeon if I don't feel up to doing the harder ones yet, and then when I do... I get punished for it. When I finally am ready to do a harder one, and succeed, I don't get to keep ANY of my reward because the bank is full, and nowhere was this explained or the capacity of the bank stated, or even that it had a capacity, until it was full and too late to do anything about it.
The administrator said I could now choose to do what I liked. However, if I do NOT do the quests in strictly linear fashion, then the bank will overflow and all the reward money is lost. This linearity should still be part of the tutorial, or at the very least the bank's extremely limited capacity should be stated, and the player warned about it.
Defeating the challenge, being victorious in a quest, and then getting slapped down with absolutely no reward at all is demoralizing.