I guess it's some royal tradition to have those poofie updo's when wearing a tiara
Well sort of. It is to give some backdrop for the tiara so it will look better and stand out from the background. Most tiara knowledgeable hair stylists know this (and how to position the tiara in a correct way) but sadly the craft is disappearing. And if you lift the hair to form a backdrop for the tiara, you're going to need to do something with the rest of the hair (unless you want to do a 60s style hairdo or a Beatrix hairdo), so an updo is the way to go. Of course this is not always done because with huge big upright tiaras it would look ridiculous.
Small comparison to explain what I mean.
Marie almost always has hair lifted to create a backdrop.
Snakey and no backdrop for the tiara (it might have actually looked better if there was). The light goes straight through it.