A great deal of this story is devoted to creating a spatial metaphor for time. In other words, Borges is trying to take an abstract, non-visual idea – time – and make a visual model for it. In fact, that's what "the garden of forking paths" is. It's a metaphor, or model, to help us envision the infinitely diverging, spreading network that Ts'ui Pen imagines time to be. And the issue of the infinite is another major theme in Borges' work.
As crazy as this all may sound, this model is considered a viable way of seeing the universe – thanks to Einstein, Schrodinger and his cat, and the quantum physicists who followed in their footsteps. [BTW, in 1957 a physicist name Hugh Everett III came up with the "many-worlds interpretation" of quantum physics, but Borges' story portrayed the same idea in 1941. You can read more about it here.]
Yu Tsun's unwavering belief in destiny is at odds with his ancestor's model of time. If all possibilities will happen in an infinite series of times, then there can be no such thing as destiny.
Yu Tsun's unwavering belief in destiny is fully compatible with Ts'ui Pen's model of time. If all possible events must happen in one time or another, then the events of his particular time are fated to happen, since they do not happen in any other time.