A design holder is trying exert her rights in the USA using EM 003220508-0001.
Is this something that can be enforceable or would she need a US design patent? What if she is registered with WIPO?
A European intellectual property right is not enforceable in the US. It is enforceable on imports into a country where the protection applies.
I can't find more information on this special design apart from this source https://www.google.de/search?sclient=psy-ab&site=&tbm=pts&source=hp&btnG=Suche&q=+++++6PetalTulip-1-L+ where the abstract of the webpage says there is a WIPO registered design, so I'll assume that is correct for the sake of providing an answer.
WIPO does not grant rights, it is merely something like a distributor. If you register a design in your country, you can use the WIPO to help you register the design in other countries (it's a little more complex than that, but that will do as an explanation). So the design in question could have had the US as one designated country in the WIPo application and the applicants could have proceeded to the national phase in the US. That means, that they could now have a US design right.
And a US design patent is enforceable in the US. However, if somewhere on the way they didn't enter the national phase in the US or the US right is not valid, then they cannot enforce the right, even if the WIPO application led to rights in other countries.
In the end, intellectual property protection is a territorial thing. WIPO is only a intermediary step to applying for national rights all over the world, it does not grant anything.