I recently tried to use the Dolphin browser login to my Trello.com account, which I had created by signing up through a Google Apps account. Since I had not set up a Trello-specific account yet, I had to try to login using Google--which automatically used the primary Google Account on my device, successfully logging me in to a different Trello account of mine. I wanted to log in to Trello using a different, secondary Google account on my device, but was not given the choice.
I'm sure the problem happens with different web sites and different mobile web browsers. Is there a solution to this? Is there some specific mobile browser, for example, that when asked to provide Google credentials will allow me to select from the available Google accounts on the device?