I tried to put a First Aid Kit beneath me just before I go down and yet I don't consume it automatically... I also tried with Swan Song Aced, dropping it during Swan Song and it didn't worked either. Is this a bug or is the discription wrong?
I suppose a fairly obvious thing to ask would be if you had checked you do indeed have the aced version? I have done it plenty of times myself thinking I have a skill only to find that the skill is not aced.
If that is not the case, I believe you have to put the first aid kit down first before going down. That would mean at least a second or two before being delivered the final blow. If you are activating Swan Song, that would mean you are already technically downed, so the first aid kit would not activate to revive you. I also believe that would be a contradiction in your skills as swan song prevents you from being downed the same as a first aid kit.