This is how the Coupe boot carpets are organised and I cannot see why there would be a huge difference between the Coupe and the Spider. But I've seen two styles and I'm not 100% sure when they cut over, early cars had press studs and later they switched to using plastic studs/clips.
There are two side carpet sections that will be in a an " L " shape each covers the rear quarter and suspension turret and then covers half the rear bulkhead, these overlap behind the spare wheel. These were secured by plastic clips but most clips have long since been snapped off and most cars I've seen have black cable ties securing them. The rear bulkhead has three hole for these clips to press in and fix the carpet in place.
The rear verticle carpet (where the number plate is fitted) is either press studs along the top section or the later style with just two retaining bolts with a large plastic star head. The rear verticle is not secured by anything at the bottom other than gravity
the the boot floor carpet keeps it in place as there should be a kink in the rear verticle where the floor carpet sits.
The polystyrene sections I've only ever seen fitted to S3 cars so maybe thats been added by someone later on in the cars history..
None of any of my Betas have had carpets glued in place, so I'd say that something that has been done by the previous owner.
I can take some pictures later on if required.... Just let me know..