It is limited to the police vehicles because all these vehicles use the same script in which the animationPhase is a float value like 0.2 , 0.4, 0.6 and so on.
The Jonzie Ambulance instead uses integer values like 2, 4, 6 and so on.

Now the problem is that due to some reasons these float values are not transferred to all clients properly. Even numbers like the ones used in the ambulance script are transfered correctly.

I assume it has something to do with bandwith optimization. Which in general is a good thing but in this special case screwed us all over :D

Anyhow if u need a quick fix just edit the scripts in your pbo's to use even numbers or round the float values to a correct value like this:
_phase = _phase * 10;
_phase = round _phase;
_phase = _phase / 10;
This yields the correct value.

But this is rather annoying work because this has to be done for every vehicle and for multiply scripts like sirens, lights and so on

Ok, we were able to find what causes this strange behaviour.
The value of the "animationPhase" which is used to determine which siren and/or which light should be on is not properly send to all clients. In our example the animationPhase = 0.2 is set for the driver and everyone else receives values like 0.2000767 which causes the switch case(0.2) to fail.

But please Bohemia elaborate why this value is not propogated correctly.

Hello, no this is an issue concerning modded police and medic cars primarily used in mods like Altis Life or Arma 3 Life or City Life RPG.