Strange step response
The step response you have is non-minimum phase. That means various things:


There are zeros (or poles, if the system is unstable) outside the unit circle (in discrete time).
The peak of the impulse response is delayed from the origin.


Below is an example showing an "ideal" delayed step, a non-minimum phase filter impulse response and the output.

As you can see, the output exhibits similar characteristics to what you have plotted.