It does seem a bit tricky before you get the hang of it, but don't worry - it's best understood in practice, but think of it as breaking down a tough problem into all it's component pieces, in order to next evaluate effectively and efficiently. The principle of MECE is to ensure that you haven't missed or double-accounted for anything.
The issue tree is helpful in your case because you can work through methodically, as you would if you were ticking through a list. It demonstrates to the interviewer that you can structure your thoughts and categorise large amounts of information.
Happy to do some sessions with you if you'd like more guidance.