When multiple logins are available, CNTL-SHIFT L works wonders. But, how does that work on an iphone?
Well, I found the answer by trial. When given the BW option (BW picked 1 of my IDs), click on the key symbol on the right. I popup appears listing all possible choices. Choose the one you want and the id/password is quickly populated just like you would want/ expect. Problem solved. With the popup, no need for CNTL-SHIFT L!