My understanding of the generator is that it works most of the time with HSL color representation. It is mostly for me to practice conversions between colors.
I first convert hex color to RGB color by taking input and take first 2 characters to represent Red value than next 2 characters represent Green value and last 2 character is Blue value. After that, I take RGB color and convert it to HSL I found Here. In the end, I just take the HSL value and change the L(lightness) value if I want darker color I subtract some value and if I want lighter color I add some value.
You can check how it looks like and plays a little with it on my codepen.
In the next few days, I will try to recreate Adobe color.