Should I wait for my inverter alarm to know when my battery is discharging beyond safe level or should I shut down the loads sooner?
Get a hydrometer and learn how to use it for detailed analysis.

For less detailed analysis, if a lead acid bank is below 2.1 volts per cell (in use) the smart money is on cutting it off if you care about long life. So if your 12 or 24V bank actually reads 12 or 24 volts, you are probably dipping below a healthy discharge level.

Better quality battery operated equipment will disconnect itself, rather than depend on you checking the voltage and taking it off-line. But we have no idea what your inverter is since you have not told us, and if it's a lower-end model it may not have a very good behavior for when it "alarms." (Even with the model information it may be hard to know unless it happens to be a well-known quality model with good documentation. Cheap junk tends not to document the things that reveal it to be cheap junk.)

Much better quality battery operated equipment will record the number of amp*hours put in and taken out (and know how big the battery bank is) rather than using the voltage as a rough yardstick.

This website provides some more food for thought, but practical and perfect don't tend to get along well in real life battery bank use scenarios. i.e. you are unlikely to disconect it for 4 hours before checking the voltage, at least in normal use. Occasionally for better numbers when doing maintenance, perhaps. 

...And voltage on the whole bank does not give you the detailed info that checking each cell will - if you don't have 12 individual 2 V batteries making up your bank, the only way to get that into is with a hydrometer.