I'd definitely take a lot longer than 20 seconds to draw my issue tree (up to 90 seconds is generally fine; I might be ok if you take 2 minutes and blow my socks off).
As for how long it take you to walk through the structure... who are your case partners? If candidate like youself, I wouldn't take their feedback as the gospel. Has a current/former consultant said that same thing? Now this is has more value already.
Walking through the structure / issue tree is supposed to help me (the interviewer) visualize how you are planning on addresssing the customer's problem. You start from the question, highlight the 2 or 3 or 4 main branches without going in detail (you go horizontal), then go back to each section and explain a little bit what sub-branches you plan on tacking there (you go vertical). Do you need to justify each of those sub-branches? Not really, at least not at length. It is good practice however to make a transition between each large branch, even if not terribly important in the grand scheme of things. Something like "once I have a good understanding of the industry, I will want to dive into the product side" will suffice.
How long should all of this take? Probably a minute, give or take. In most instances, we know how good the candidate will be after just hearing the issue tree walk through. Rush it, or jumble it, and we know you will struggle.
Hope this helps -