Hi we recently purchased a house which was fully renovated

You need to formally become resident at the comune, never heard of any “2 month” bit, you have to become  resident!

As Steve says, to get the 4% rate it needs to be your prima casa, and you need to be resident in the comune,  i.e. - it is your principal home.  2 months has nothing to do with it.  

see >  https://www.lifeinitaly.it/Inglese/italyresidenceguide.htm