I will start by showing the issue so it's super clear what the problem is:
Alright. So the cup has fluid type effector, with Effector type Collision.
The cup is parented to the plate so they will act as one.
The plate then has a rigid body so it will fall and is also an effector so the liquid should interact with it once it spills over (that was the idea xD). Here are the settings for the plate.
Then we have the domain which is baked and then the meshes are baked with rather ok settings I guess (I followed a bunch of tutorials and draw some conclusions myself).
And that's all the info I think should be needed. So, how come the liquid is still just falling down through the cup?