Lots of inyanim on this question and I’m not aware of any single answer. I’ve heard its a rosh chodesh minhag at some Sephardeshe shuls but certainly not all.
If we read literally the last phrase of this pasuk, Uvayom simchaschem ovamo’adaychem ovaroshei chodshaychem”, we might think it was done during z’man beis hamikdash but NOT after curban bayis sheini. Perhaps some sehphardeshe shuls have instituted monthly blowing l’ zecher limikdash.
Also the pasuk תקעו בחדש שופר בכסה ליום חגנו could be read to mean Rosh Hashana and not every rosh chodesh.
There are probably lots more explanations I’ve never heard.