What a fantastic home for two little finches! Of course, you now have plenty of room to add more.
When I had a walk-in aviary for a while, I just turned the birds loose in there cold turkey. They had the same feeders they had always had (seed hoppers), just in different places, and it didn't take them any time to find them. Same with the waterers, I used the same tube waterers they were used to, and so the transition was pretty easy. As long as you leave their old cage in the doorway, they will probably continue to use it. I would take away the cage completely, and then watch to see how they do. The feeder is quite high, you might want to put it on the floor and then gradually move it up, but the birds find their way around pretty quickly. That's awesome that they went right for that nest!
And welcome to the forum! There's lots of good reading at the Finch Information Center, linked at left, and the members are always ready to answer questions. We have quite a few members from Georgia.
I recently bought a secondhand wood and plexiglass aviary, cleaned it up, and decorated it for my little peeps ☺ (a pair of RCCBs). I am so happy to give them the extra room and a more natural-looking environment. On Monday, I put their old cage on the floor of the new aviary and opened the door of their old cage so they could fly out of it and explore the new aviary with the comfort of retreating into their old cage if desired. A few hours later, I realized that they were exploring the floor only and didn't see the top half of the aviary, so I took a different approach. I positioned the old cage on a table and lined it up against the side door of the aviary (aviary door open) and blocked the bottom and top ends (see picture) and made sure the entire room itself was bird-safe. Doing this allowed them to fly up and discover the top branches. They are very excited about their new digs and have started building a nest in the grapevine globe. They also take baths, snag nesting material, and eat food from the dishes at the bottom of the aviary, but they haven’t discovered the hanging bird feeder at the top or the other nests along the back wall. They still go into the old cage to eat from the feeder/dishes and cuddle/preen on their favorite perch. And in the evening, they still sleep in their old cage. 
My question is when should I remove the old cage? When they stop sleeping in it at night? When they complete their new nest in the grapevine globe located in the aviary and start sleeping there? I worry about taking away their old cage too soon and causing them distress. Your opinion/advice is greatly appreciated! 
