I wonder, if I put a wipe on an object, so it comes in on a background, the background wipes with the effect.
What's going wrong, it it possible to make it so, that the background is straight and the object comes in with the effect?
I had to read your post twice to understand what you are saying. It appears that you have a background video layer and another clip above it and you want to put a wipe on the clip above to make it appear over the background clip below.
If this is the case it sounds like you're using an effect with a Dropzone layer and that Dropzone layer will affect all video below. Right-click on that effect to Open in Motion, delete the Dropzone and save under another name.
Or, try putting the upper layer in a Compound Clip. Then open the Compound Clip on its own timeline and put the effect on the clip there. Sometimes the Compound Clip will isolate the effect.