Late to the party, but here are some other questions, just kinda random, but thinks to look at/find out.
What was the radio and controller brand and model of the old system?
Who was the company/contractor who put in the system? (I know, this may open a can of worms)
Just a thought, are there any audio adjustments between the audio output of the radio and the input to the siren controller? My point is, if audio levels coming into the decoder apparatus are too high, the circuitry may not work properly; distortion will kill decoder accuracy.
What does the 911 center say they are sending for tones, and the timing? And the audio level, aka frequency deviation? These will be important numbers.
FWIW, I once had a conversation with a mfr's engineer about tone paging, and his basic message was 2-tone paging systems are really pretty loose, in order to accommodate all the other decoder manufacturers out there. Oh, your decoder responds to different timings? No problem, we'll make it work. Because the pageout is important, not adherence to the 'stanard' (whoever has defined that).
Just a FWIW, the BW, Bandwidth, is how far from the center frequency one tone is supposed to be allowed; example, your A-tone is supposed to be 496.8 Hz, it could go as low as 484.7, Hz, or as high as 509.2 Hz, that's +/- 2.5%. This figure is also important in whether adjacent tones are within or outside of that 2.5% either side of center.
Another important figure is the audio level, called FM deviation, of the transmitter. Industry standard is supposed to be 60% of channel peak deviation. Ever since the narrowbanding deadline of Jan 2013, peck deviation has been 2.5 KHz, and 60% of that is 1.5 KHz, deviation of the tones. That's the deviation level your 911's transmitter should be reaching. Go too hot, like 2.2, 2.3, 2.4, or 2.5 KHz deviation and the resulting distortion at the receiving radio will cause poor decoding. Likewise, if the transmitter deviation of tones is small, like 0.5KHz, will cause decode problems. But again, I've seen lots of systems with enough 'slop' in them to accept a wide range of levels.
As far as timing, a realllll long time ago I heard about an (unmanned) fire station, whose tones were like this: the A-tone was actually the B-tone of one station, (lets call it station 1) and its B-tone was the A-tone of another station (we'll call it station 3). The idea was if station 1 was paged out, then station 3, Station 2 would decode the correct A-B set, even tho the tones coming in were 3 seconds of A, and 1 second of B!
Another anecdote, City of Raleigh NC, while I was working in their own radio shop; sometimes a station would report a pageout (lights turned on, speakers opened) but they weren't dispatched. My colleague and I were working in one station one day, and suddenly the lights turned on and speakers opened up, even tho that station hadn't been paged. It had picked up the B-then-A tones from 2 other stations on the other side of the city, paged in a certain sequence. We looked at each other and said "What the hell just happened???!!!"

The short version was that tones for new stations had just been picked at random over the years, and we found about 6 different stations out of 27 that had these conflicts. It was just a minor annoyance to FF's, because it was comparatively rare occurance. We did end up re-jiggering the whole tone set for the entire city and got rid of all conflicts.
The final of all this, and this is my opinion only, but you need to have a combined meeting with the siren manufacturer, the radio shop and the 911 center. Perhaps some knocking of heads, but this is ultimately solvable. there's too much finger pointing. (the bane of so many problems).