And I still don't understand what 'start attack immediately' does. What's different from increasing the attack shape? Attack starts acting on the 2nd sample of a burst, does it now also include the 1st one (which would only have a very minor effect)?
The attack does indeed start right away. However, it starts very slowly, and ramps up to the target speed slowly (depending on how far it needs to travel and the user set attack). With this new setting, the attack speed immediately gets set to the target speed. If you run some waveforms, you can see a pretty pronounced difference, especially for compressors with long attack times.
What's the benefit of using this control? Attack characteristics mimic what the ear expects, rather than the alternative, which is that a sudden burst of sound comes in and at first the compressor does seemingly nothing at all, and then dips down later. Of course, the compressor needs to attack to the same place either way, but our ears notice it less when it happens right when the burst of audio kicks in, rather than a moment later.