Trapping an rasterize image

I don't know why you need to, but make a box exactly the same size as the image and give it a center stroke of twice your desired trap, then click overprint stroke in the attributes panel...

Personally, I don't see a need to trap this situation at all, unless your background colour is meant to be output as a spot colour (e.g. a Pantone). In which case, the easiest thing to do is to make a copy of the clipping path around the picture and paste it in front (Cmd-F) and give it a .2 pt stroke of the purple and make that stroke overprint.

However, if this file is being printed in CMYK, since trapping is used to prevent "gaps" that would be caused by misregistration, if you think about it, when this graphic is printed in CMYK, there are no gaps. There's Cyan in both the background and picture, there's Magenta in both, there's Yellow in both. Even if this was wildly out of reigister, The only one that could even create a problem is the Black, but it's so light it would never show.

The trap I see in the sample from your contact almost appears to me to be a post-trapping PDF from an actual RIP (the RIPs I have worked on in the past had this ability) so I'm curious.

If you are doing this for print, I would check with your printer to see if it's necessary. Most modern RIPS will do trapping  and adding a manual one tends to complicate the process.

What's your intent?

I don't think you can apply the trap effect to a raster image, but you could give it a mask, apply a stroke to the mask, then set the stroke to overprint.