[Philipp Figueroa] “I guess this might have something to do with the anamorphic footage I am using but i would expect FCP to render/ compress it to the right aspect ratio as soon as I outplay. “
No, it doesn’t work that way. The only thing FCP does is change the canvas and viewer to show the anamorphic video with a stretch applied. It’s not affecting the original source files, simply distorting them on the screen to make them look correct.
Export a Quicktime movie of your FCP project. Don’t use “Quicktime conversion,” just use the top choice, “export Quicktime movie.” This creates a movie file of your project using the current project settings.
Next, open the exported Quicktime file in Compressor and convert the anamorphic source video to a square pixel 16:9 aspect ratio movie. 640×360 would be ideal. Compressor has several options for dealing with rescaling and cropping footage.
I recommend opening up the Compressor manual spending some quality time with it.