Your inverter doesn't do any kind of auto voltage regulation,more over it gives a square wave output.
Only a UPS or stabilizer will do AVR .
To put in other words, not all UPSs are inline, in the sense that you are not drawing the power through the UPS all the time, i.e. it acts (supplies power) only when the mains power is not available, otherwise it just idle or charge the battery. Because of this offline-UPSs cannot provide any protection against surges and variation in voltage levels.
It is most likely that you have the offline-UPS without any Regulator and Surge protection.
I personally prefer to just use a surge protector as I live in an apt. whrein the loads are pretty much constant and would have a local transformer. Otherwise you better get something that can provide both regulation and surge protection. Or first connect a surge protector to the wall outlet and then connect the stabilizer to the surge protector.