I would very carefully check the wires to see if any are loose or maybe pulled out of the connectors that go under the screw terminals. The cancel button breaks the circuit to the relays, making them release early; before the 1-minute (or 3-minute, which ever yours has) cam gets around to click the "off" microswitch.
When you say about the output, the voltage you see on the siren control terminals is actually not important. What happens is that when the timer triggers the siren, those two terminals get connected together by the relays. It's just acting like an on-off switch. Here's a picture of two jumpers that you need if you don't have a radio/tone receiver attached: Note that this is an AR timer, but I believe the jumpers are the same as the AF.
I wish I could see it in person, as I'm sure I could help you better that way.
Charles