Q.When To Spray The Non Fruit Cherry Trees?
Last year is my first year with this tree. Worms were coming down on what looked like a string. What should i do?

Certified GKH Gardening Expert
Sounds like caterpillars of some sort. Your photo did not come through, so I will not be able to identify them.
You shouldn't need to do much of anything, unless the tree is being covered with webbing, or the flowers and leaves are being eaten faster than they can bud out.
Should you feel that spraying is necessary, timing will depend on on what you use.
Dormant oils should be used during winter dormancy, where as more of the organic solutions can be used any time of year.
Just be careful if you plan to use Neem oil. Using in bright light, or hot weather will guarantee that your trees get fried, crispy!
These articles will help:
https://www.gardeningknowhow.com/special/organic/what-are-organic-pesticides.htm
https://www.gardeningknowhow.com/edible/fruits/fegen/dormant-oil-information.htm