Start at the bottom
It all starts with the little guys when you are talking about ecosystems. Bacteria, mold, etc etc etc. Single celled organisms.
To spread your Eden you are going to have to do a few things.
However you managed to create your little green space you will spread from there. This will happen naturally if you protect the environment around your Eden and maintain the balance of the ecosystem. Maintaining the balance in an ecosystem is no small task...the smaller the system the less it can absorb system stress.
Prep the battle field (so to speak). Plants require certain minerals and organics to survive. Spread them around the radius. This will include minerals which could be mined from your terraformed planet as well as organic matter/bacteria etc which could be grown/cloned. Don't forget the insects. Once the organics and microscopic organisms are up and running add bugs.
These things (if you maintain the system) will gradually spread on their own, at a certain critical point you won't be able to effectively impact the ecosystem anymore as it will grow to be self sufficient.
Thats how building the system would work. I must re-iterate that this is incredibly difficult, the intricacies of ecosystems are still way more complicated than we understand. Rarely do you see a situations where humans 'helping' and ecosystem actually helps (with the exception of clean-up operations). Mainly I am referring to killing off predators or culling herbivores etc etc etc. Anyway, rant aside...
You can't just have a bunch of oxygen floating around in the atmosphere. Its pretty dang flammable...like a lot.
The atmospheric composition of earth is a mix of course and you would need the same mix, or at least close to the same to create what you are talking about. Its tough for me to ignore the idea that you just BAM have an atmosphere like earth but no life on the planet.
Planting outside the zone. If you have the atmosphere, all you need are nutrients (compost) and water and the correct temperature range/light (lat/lon). Super easy...I mean relatively speaking.
In reality to terraform you would probably have to start with domes for people to live, each dome (you'd need many many many of them) would have a gas farm...which skipping the obvious fart jokes would help modify the atmosphere to something tolerable for plants, bacteria, insects etc. Over time the farms aren't necessary as the plants will spread etc etc etc.