That doesn't always work because they've referenced elements of previous videos before spinning for the next one ala a step ladder in wheel 6. Just like with BotW I imagine they watch all 3 films back to back, but I feel the spins we see are sometimes staged recreations of probably real spins off camera or cut footage.
ok, so then maybe they do this:
They shoot the intro
Spin the wheel on camera and 3 videos are chosen, no contextual jokes typically, but they do their little "lets go watch it!" thing
They watch the videos
they go back and do the transition bits for in between videos.
discussion after everything
i have to re-examine the latest episode a bit but i dont remember if they ever go one shot directly from doing a little "transition" bit to spinning the wheel without a cut. they always cut closer to the video anyway, so who knows what the hell is happening.
anyway, thats how i would probably logistically shoot it if i were doing the production, personally. in my head i just feel like its definitely not "shown as shot" and there's some logistical time saving involved in the production somewhere. also, if they did it like this it would be easier to "hide" that they chose something on purpose if they ever do