After spending hours of dissecting Oz’s performances and carefully picking out how he does his tricks I can confidently explain that I have absolutely no idea how this works
youtube dude was right, many of his tricks are based around sneakily writing something down or inserting something in a "sealed" place while distracting you. Last trick he is clearly writing down that information while doing the chair trick. Other tricks like the cups are technology-based, probably haptic feedback of some kind. He only answers when the cups are placed down again.
America's Got Talent | Oz Pearlman | All Performances