Birdpoppy
There could be many reasons as to why your Zebras died, and very difficult to pin point what happened without all the facts.
You need to look at:
Diet
Environment
Temperatures
Air quality
Diet: A good quality Finch seed mix, fresh greens, vegetables and some fruit, fresh water, bird grit, cuttle bone, hard boiled eggs, bird vitamins in drinking water, and spray millet.
Environment: Would have to do with the enclosure itself. Did they have sunlight, access to shade, too much humidity, drafts.
Temperatures: Although Zebras are hardy little birds, a lot depends on what they were used to before coming to live with you. Most Finches, enjoy temperatures of around 20 to 22 degrees Celsius. They can be acclimated to lower temperatures, but it has to be done gradually.
Air quality: The air quality in a green house, can be iffy for finches. Sprays might be used, residual pesticides can linger in the air and be deadly.
So all these things can be contributers to all sorts of problems that would cause illness and death.
By the way, just a quick word of caution : if you are thinking of building an aviary, Finches and Hookbills should not be housed together. Hookbills can very easily injure and kill Finches.
Hope this I formation was helpful.