This could also be a load issue. For a SSR based dimmer to work properly they need to have a heavy enough load. LEDs because of the small current draw can cause dimming issues like this. As a test, if the other suggestions don't correct this, connect a 100W light bulb to the string. This is called a "ghost load" and should smooth out the dimming of the entire string and make things work correctly.
A 100-watt bulb is a lot more than a "ghost load". That will draw over eight-tenths of an amp by itself.