Relationship between Poisson and Uniform distribution

Question

I'm reading this book and on page 565 he solved an example about the Kolmogorov-Smirnov test:

I have two questions:

1. What Poisson distribution has to do with uniform distribution in this context?
2. Why is he including the difference $|F(x_i)-F_n(x_{i-1})|$ to find the Kolmogorov-Smirnov statistic $T=\sup_{t} |F_n(t)-F(t)|$? we only need to calculate the supremum of the $|F(x_i)-F_n(x_{i})|$, no?