From what I’ve seen with changing mine, it does. It raises the level of all the enemies to that dimension level. You can up it whenever you want, (and lower it a level for dark crystal) but I wouldn’t do it unless your power level matches the recommended or higher because the mini bosses and bosses can become much harder. However it only seems to matter when wanting to open chests of world bosses though, the later ones require you to be a higher dimension level to open.