No, there is no new process that makes aluminum ride different.
And to be perfectly clear, "aluminum" doesn't ride harsh. Oversized aluminum rides harsh (Klein, Cannondale), skinny tube aluminum bikes (Vitus) ride soft.
Aluminum is a low density metal, so compared to something like steel, you can decrease weight by increasing the stiffness of the tubing by increasing diameter without making the tube walls too thin for practicality. So making a very light and reasonably stiff bike involves making the tube diameter very large. You can try to do the same with steel, but you end up with dangerously thin tube walls.
Ultimately, the lightest practical bicycle tube is going to be the one that is as wide and thin walled as is possible. Aluminum, magnesium and carbon do this better than titanium or steel. But with the right engineering, all can be very light.
Otherwise, the old aluminum Treks like the 1400 road bike are examples of moderately light, moderately stiff and not harsh riding aluminum bikes. And Cannondale, starting with the 3.0 generation, mixed tube diameters to remove some of the vertical harshness while keeping the drivetrain stiff and light.