Im nt in a stat board but one rule is clear - the govt never owes.

Basically if u join 1 march u w get salary on 10 march for the whole month from 1 march until 31 march.

If you join after 10 march eg 11 march you will get the last mth from 11 mar to 31 mar on 10 april plus the whole mth salary from 1 april to 30 april.

That is how it works in my ministry. The date differ but the basic principle does not. The only deviation is when you resign then the organisation will prorate it to the number of days that remain in the month in which you leave.

You might want to check with your HR again.