There is nothing wrong with or strange about seeing interlacing if you shot 1080i50. If you were watching your video on a broadcast monitor instead of on the computer display, you would not see the interlacing. Computer monitors cannot properly display interlaced material, which is why you see lines.
I’m not sure why FCP is using 1080p24 for the sequence setting, because your sequence settings need to match the format you shot, which is 1920x1080i50. Change your sequence settings to ProRes 422 1920×1080 50i.
What is your final delivery medium? Web? DVD? If you are exporting for web, don’t use FCP’s deinterlacing filter. Just edit your video, render, export a Quicktime movie (uncheck self-contained) and open the exported Quicktime in Compressor.
When you compress your video for the web, you can use Compressor to create a deinterlaced 25p video file. Turn frame controls on in the motion tab of the inspector window. Change Resize to Best, Output Fields to Progressive, and Deinterlace to Better or Best. Compressor’s deinterlacing is much better than FCP’s deinterlacing filter.
If you are making a DVD, there is no need to deinterlace your video. It will look fine when played back on a standalone DVD player connected to a TV set, and most decent DVD playback applications on computers have built-in realtime deinterlacing algorithms.