Why juice when light switch is off

In my basement there's an 8ft florescent light and it stopped working the other day. No flickering, no warning, just stopped working. I figure it's probably the bulbs so I'll get some more. But I plug in my tester to make sure the switch is working and the tester lights when I turn it on and goes off when I turn it off. The part I don't understand is the light plug is always showing hot using my other tester. It doesn't matter if I switch between the two plugs in the outlet. I would have thought the cord to the light would show green when the switch is off.