Is the timebase 100ps per division in the picture?
100ps/div would be indeed cool, but given that this is supposed to be the impulse response of a Tektronix 485 (-> 350 MHz), I'm afraid your guess is not realistic and rather an order of magnitude too low.
So the 100ps pulse has been "smeared out" to become 10x wider?
Yes, smearing out a sharp pulse is expected to happen in a low pass
causal filter, and if we consider those 100ps to be practically zero time, what we see in the image is the
impulse response of the system (filter, oscilloscope, whatever), h(t).
For an intuitive approach, you can think of the low pass filter like a system with a "speed limit" in energy transfer speed (the system is not allowed high frequency, or high speed transfers, only slow exchanges). Now, if you suddenly drop a lump of energy (that 100ps pulse) in such a filter, the energy exchange "speed limit" will make that lump of energy to stay there for a while, until the circuit somehow manages to deal with it, therefore the smearing in time of the initially very narrow pulse.
Note the
causal word in the name "causal filter". A causal filter will never produce wiggles in front of a signal, while a DSP filter might produce such artifacts. As an example, Fourier transform is not causal. If you use Fourier to implement a filter, such a filter will produce some fake (artifacts) output
before you even start to apply your signal. That's not how physics works. Other way to look at it is to say one can not do a Fourier transform live (in real time).
In the next image, you see before each edge some fake wiggling.
That is because of non-causal DSP. Analog oscilloscopes never show that kind of artifacts, because they are made with physical analog components. Physical world is always causal.
Back to the impulse response, h(t), of that analogue oscilloscope
that wiggling waveform completely characterizes the time response of a system. Starting from it, one can deduce the time response (the waveform) for any shape of a given input signal (or else said, deduce what distorted waveshape we will see on that oscilloscope's display when we apply an arbitrary waveform input).