kcdzim put it quite succinctly.
I won’t use the quote function because it will all be in small print with blue background, so I’ll just cite the source. This is from kcdzim:
Dutch territories are treated exactly the same as any other territory that is
a) friendly
b) lost their capitol.
The only difference between Dutch territories and say, French territories after Paris has been lost, is that the UK/Anzac have a special relationship that allows them to take control of them before they’ve been captured by moving a ground unit into it. Typically you need to capture - this is the one of the two instances where control of a friendly territory passes to a friendly power. The other instance is a neutral that has been attacked but not captured.
So when you’re confused about things, ask yourself how you’d treat normandy if it were still french.
Can you UK/Anzac/US/Russia land a plane there? Yes, as long as it started the turn friendly and they’re not neutral. Exactly the same as any other friendly territory.
The US is not barred from being in a dutch territory - they must be at war first, but then they’re allowed to move into it just like any other friendly territory.
I will add one direct statement in an attempt to improve understanding and clarity:
The USA can NOT take control of a Dutch territory the way UK/ANZ can. The only way for the USA to control a territory that was originally Dutch is if an Axis power takes it first. Then if the USA takes it, they will control it.