I had both a fat and bony decompression. I think the information you received is wrong, unless the person was referring to a decompression that is performed while still in the active/hot phase of TED.
I woke up from surgery with immediate relief and noticeable results. My entire face was pretty swollen for about two weeks, which became unnoticeable after a month, but there was no orbital swelling as I had been in the cold phase for a year before the surgery.
I posted all about my OD on my blog, which include a daily photo update and before & after photos. PM me if you want the link.