In Rocket League when you get 5 common items you can trade them in for a rare item. When I get decals I never seem to find them in the customization tab. Everything else I get from trade-ins I seem to find.
And I am sure it is supposed to be equipped. Because its description says:
When equipped, the item keeps track of how many saves you get.
In my experience I have received decals for DLC cars via the trade-in system, for example, I got the Royal decal for the Dominus. So if you do not have the DLC car for which the decal is for then you will not be able to use it, however you will still be able to trade it in.
When you get a rare decals it will say which car this paint job is for. You are not able to just equip these to any car you want as they are car specific and can only be used on that one specific car. You can see which car they are for by going to garage and selecting the bottom option which will take you to all of your uncommon, rare and very rare toppers, trials and decals.