Lawyers and property managers help out here.

If someone pays the First Rent let's say January but was not able to move into the property due to the repairs the landlord was doing in the property and later moved in February after the repairs.

When does the person rent starts to count.?
On which month is should the next rent be paid; January or February?
Note: No reciept was issued for the rent but there's evidence of payment.

You rent starts the day you pay

Omihanifa:
You rent starts the day you pay

Even if the house is not ready for you to take possession
Is this the position of the law?

Sorry, the moment you pay, you initiated the rent contract. The exception will be if this is a signing clause that spelled out the terms of agreement before you made the payment. As said by you, there isn't such. Pay your landlord and continue to be a good tenant. You will build your own soon