Actually yes, ive just seen the Alarm Panel....(attached)....i'm pretty sure if i remove power and batteries to my smoke detector it will trigger something...alarms may go off
Yep that indeed looks like a fire alarm panel. They are smart enough to detect sensors disappearing off the bus. Typically these central fire detection systems are also connected to a remote monitoring location. Here typically only large buildings have these and they will automatically alert security staff to go check the situation or in some cases also escalate it to the fire department. So if that is the case you might not only be annoying your neighbor, but i would guess if this was the case they would have also explained upon renting to you how to clear the alert in the event of a false alarm
So yeah as previously said stick a bowl, glove, bag etc... over the detector.
EDIT:
Anyway, invest in some heat resistant matting since you're either burning the table underneath, or you are using too much flux. Although it's often impossible to use too much flux, in this situation it is.
No such thing as too much flux
But yeah soldering makes smoke and i seen some really sensitive smoke detectors that will go off at just a little squirt of deodorant or hair spray. Luckily the detectors at where i work are not one of those, we make plenty of soldering smoke here and there and they never went off.