Romania is part of the EU (European Union). The EU has open borders. You can come in from anywhere without a passport basically. It's not like going to the US or China or somewhere with stricter border controls. I know that people like to pretend that we have open borders in the US, but we don't. I know this from personal experience. I've crossed EU borders many times before. They actually are OPEN. Ours are controlled. Not completely closed, but controlled.
Technically, Romania isn't officially part of the Schengen Agreement, but effectively it's very easy for people like Tate to get in and out of the country. Romania is part of the EU and borders several Schengen countries. There's lots of travel between Romania and neighboring/regional states and Europe as a whole. Romania is poor by European standards and lots of their citizens work throughout Europe as well as the US and other more developed countries. Their borders are not well controlled and much of it is by design, some by corruption or incompetence or convenience.
Sources/relevant information:
https://en.wikipedia.org/wiki/Schengen_Agreement
https://en.wikipedia.org/wiki/European_Union
https://en.wikipedia.org/wiki/Romanian_diaspora
https://en.wikipedia.org/wiki/Open_border
https://en.wikipedia.org/wiki/Open_border#Examples_of_controlled_borders
https://en.wikipedia.org/wiki/Open_border#Examples_of_closed_borders