Min stands for minimum dimness that is allowed, when the computed value (from automatic cycle) is below the min (aka min) reef-pi will set the value to 0 (or start if set). This is to safeguard lights from flickering at low voltage. For example you cant dim kessil to very low, (13% is lowest that i have experienced), below this (that is 1.3V) kessil lights will start flickering. The same thing exist for several other LED lights as well. So, I recommend using the "min" (aka minimum) threshold to use in such cases.
The "start" configuration is set the origin or start of the dimming range. Normally it 0-99, if you set start to 1 then it will be 1-99. Reason start exist is, in some wiring scenarios you may see 0% pwm leading to 100% brightness (the underlying reason being some chips implement the variation as a cycle).
To summarize: When you make a lighting controller test it with 0-100% variation using the reef-pi slider, if you see your light is full bright at 0%, use the "start" configuration (set it to 1) to ensure the light is indeed off when you set 0% in slider (since reef-pi will now set 1 instead of 0)
If you see the light is flickering at low %, then increase the dimming % till you see its not flickering anymore, and thats your "min" configuration.
Does this make sense?