Jake did beat Eva to the cafeteria. He didn't need time at all to change, but he did change at a fairly normal rate. Or as normally as he could manage with the prospect of food ahead of him. He wore civies and his goggles still dangled around his neck. Yeah, there was that massive concern about secret IDs even within the league, but there had to be some sort of trust within them. It had taken him a while to figure that out - but he had to trust someone. Especially the people he was working with.
He'd gone down to the cafeteria, knowing Eva would catch up with him. It was good to know that. New relationships were weird because there were all those boundaries and limits and reactions left for you to figure out, but most of that knowledge - between Jake and Eva - they'd already figured out. It made things easier, not to have to worry.
Jake loved cafeteria food. He liked the speed at which it was delivered mostly. Food was his first love, really. It was about the smell. The way it enveloped you so thoroughly you could basically taste it on your tongue before even having taken a bite. So when he met Eva, he was beaming, because if home was anywhere - it was in a cafeteria. It was his happy place. "Have I mentioned today yet how awesome it is we have a cafeteria this close to us? It's like a literal second in walking distance."