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If your tree is doing well then it doesn't need fertilizer according to Texas A&M Horticulture Extension. If you fertilize your lawn, then some of this is being picked up by your tulip poplar. Excessive fertilizer, particularly nitrogen, results in fast but weak growth. Forest soil is often very rich from decades of decomposing leaves and wood, natural compost. If you wish, you can use a spreader to apply compost to the lawn. Remember that tree roots extend beyond the drip line by about 50%. That means if it is 10 feet from the trunk out to the edge of the branch tips, tree roots extend 15 feet from the trunk. (This is also important to know when watering.) Allowing grass clippings to remain on the lawn to decompose is another way to slowly add fertilizer. If your tree were doing poorly, I would suggest a soil test to determine what, if any, nutrients are deficient. Fertilization of a healthy tree is not necessary. There are products specifically labeled for trees
https://www.gardeningknowhow.com/ornamental/trees/tulip-tree/growing-tulip-trees.htm
https://aggie-horticulture.tamu.edu/earthkind/landscape/fertilizing-woody-ornamentals/

In N.C., tulip trees typically flower before other deciduous trees leaf out. Look for swelling leaf buds on the branches. If you see none, that's not a good sign. Do small branches snap off when bent instead of bending? If you scratch a small, thin area of bark, do you see green tree tissue? Poor planting technique may not show up immediately. Contact the seller to see if there is a one year warranty. How to do a scratch test is covered in this article: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

This article will help you.
https://www.gardeningknowhow.com/ornamental/trees/tulip-tree/growing-tulip-trees.htm

A tulip poplar grows up to 90 feet and probably wouldn't do well in pot culture, which is better suited to small or dwarf trees and shrubs. You are in zone 8a so a tree should do fine during the winter in your area in a large container.

Here are tips to growing trees in pots:
https://www.gardeningknowhow.com/ornamental/trees/tgen/growing-trees-in-containers.htm

Black tulip tree is really a magnolia so all the magnolia care instructions apply. The "tulip" is not related to tulip tree, Liriodendron tulipifera. The "tulip" refers to the shape of the flower. The link below goes to magnolia tree care. Use the website's search feature if you have other questions as there are many articles on this popular ornamental tree.
https://www.gardeningknowhow.com/ornamental/trees/magnolia/magnolia-tree-care.htm

Classic symptoms of Verticillium Wilt! Here is an article that will help:

https://www.gardeningknowhow.com/plant-problems/disease/verticillium-wilt-treatment.htm