Yes it does. Not only that but the voltage out of that light controller can vary anywhere between 0V and 30V (AC I think) depending on the pattern the lights are displaying. So it is not even compatible with the low voltage sonoff. Assuming it is one of the ‘7 pattern’ type sets of lights.
The way to automate the lights is to plug them into a smart socket like the sonoff S26 series. Note, I’m not particularly happy with the S26. The sensitivity of wifi reception is rather poor compared to other options. But other recommendations depend where you live.
The LED string itself is likely 5 VDC pr 12 VDC. What does the adapter say?
I am doing something similar. I am using standard mono-chromatic 5VDC fairy lights on the Xmas tree and I plan to control them (fading and so forth) with a ESP8266 NodedMCU. I am using a FET connected to the PWM output to control the light. So far the light can turn on-off-dim from HASS, but I want to be able to program automated fade-in fade-out patterns in ESPHome itself. That will take some Lambdas, which I know nothing about…