Technically you only need hub rings to install wheels. The process used to be that you put a hub ring on, tighten the wheel, then remove the hub ring. This ensured that the wheel was perfectly centered once the lugs are tightened. If your wheel is moving around after the lugs are tightened then you should be more concerned about the play in the wheel, the lug or the bolt.
Your wheels are either hub centric (centered using the hub) or lug centric (centred using the lug). most jap wheels should be lug centric with a wider hub hole to allow for varying axles.
So you'd kinda sound like a tard if you went to a tyre shop and told em that you want them to leave the centering tool in it after they're done. "Oh yeah, leave the cast on my broken arm on after it's healed, it adds strength to my arm".
Hub adapters on the other hand need to be hubcentric, as they aren't as lug centric as wheels are.
Lug centric wheel + lug centric hub adapter = fail
Lug centric wheel + hub centric hub adapter = win
Lug centric wheel + hub + no hub ring = win
Hub centric wheel + hub + no hub ring = fail
Hub centric wheel + hub + hub ring = win
kapish?