My wife's old Seiko Hi-Beat started running fast, so I thought perhaps it had become magnetized. I put it near a compass, and sure enough the needle was attracted to it. So I ordered a vintage demagnetizer on eBay, one that specified "alternate" current only, not direct, from the early 1900's when the battle between Edison and Tesla was still raging. Then I started thinking. A compass needle is magnetic, and will be attracted to ferrous metal, whether the metal is magnetized or not. Sure enough, all of my watches attracted the compass needle. They could all be magnetized, but I doubt it. I fear I'm missing something obvious, but I wonder: how can the compass test be valid, given that any ferrous metal will attract the needle?
You need to sprinkle some fine iron filings on a sheet of paper and then move your watch beneath it. If the filings jump around your watch is a magnet. Or maybe it's not, could just be very low amplitude indicating the need for a service. Anyway, you've bought the demag so just whack the watch through it before you get it serviced.
I've always heard if you are going to use a compass you have to demagnetize it first. Then if the needle moves the watch is magnetized.