Plums, peaches, and cherries are usually grafted via bud grafts. A single bud is removed from the original tree, and implanted into young growth on the new tree. The original tree is not productive, while the variety for this bud, Shiro, produces large numbers of very juicy, very sweet plums that are almost like eating candy. As the bud grows into a branch, the part of the branch distant to the bud will be removed, resulting in a branch of Shiro instead of the original. That usually takes one or two years.
The point where yellow leaf stem (petiole) meets green bud, is the abcission layer. If the bud didn't take, the whole thing would dry out. As it is, loosing the petiole while the bud itself is green, is a sign the bud has become one with its host, and will soon be growing nicely.