I think you are forgetting a part with that Christmas light, you also need to by something
like this to control that light string. And those "starter cable" will regulate the output to the leds. So, if you change the voltage at the input. The led dimmer controller will not response will to that.
Also, by the look of the dimmer that you have chosen. It look like it is NOT SAVE to use for you. Because the layout of that board is not good.
The clearance between the life side (high voltage part) and your Rpi connection is not at a save distance from each other.
I don't know your knowledge about this topic. But a other possibility could be that you use a dimmer that can be used with you lights. (for example the link that I provided*). And modifide it, so that you can control it with your Rpi. For example a save way of doing this could be this: you buy something like this solenoid
that would push the bottom of the controller. In this way you can dim the light in a save way. And you could mount as a bonus a ldr (or other light sensor) to one of the light in the Christmas light. Than you can check if is on or off.
*not 100% if it is the correct one for you