I don't understand the excerpt below.
The trivial bundles were defined as split epimorphisms, and since the ground category was additive with kernels (in fact abelian), they are the same as product projections. This is exactly how algebraic topologists define the trivial bundles in the category $\mathbf{Top}$ of topological spaces, as the product projections. But since $\mathbf{Top}$ is far from being additive, they are far from being just split epimorphisms, as one can see from simple geometrical picture of course.
What is meant by "far from being just split epimorphisms", and what "simple geometrical picture" can demonstrate this?
A split epi in $\mathbf{Top}$ need not even be a fiber bundle at all: its fibers don't have to all be homeomorphic. For instance, consider the map $p:[0,1]\to[0,1]$ given by $p(x)=\min(2x,1)$. This is a split epi (it is split by $x\mapsto x/2$), but $p^{-1}(\{1\})=[1/2,1]$ is an entire interval while the other fibers of $p$ are all single points.