HCCI isn't diesel, nor does it have a spark.
The "homogenous" means that the air and fuel are intimately mixed. A diesel has a stream of injected fuel that has to mix with the air, and won't burn until the local mixture is goldilocks "just right". Means that there's a bunch of air that hasn't seen fuel, and a bunch of fuel that hasn't seen air. In the "just right" zone, the temperatures are similar to those that you would see with stoichiometric combustion, even 'though the total package is running very lean....there's your NOx. In the middle of the fuel stream, there's plenty of fuel that never gets hot enough to completely oxidise, so you get soot.
Spark ignition can be homogenous, but to avoid knock needs low compression.
So this takes the efficiency of high compression, and the cooler combustion of the same fuel load spread evenly over the air.
As to how they do it ???
Not sure...have seen some dinky piston arrangements that have like a "fire piston" that rapidly compresses a small portion of the mixture (think those piston fire lighters), which then spreads into the main charge...the small piston basically "detonates", and the flame is then spread into the main charge.