Dear Tushar
Your query is covered under Section 10(1)(b) of IGST Act - place of supply of goods -
When goods are supplied and delivered to the same state, but the billing is done to customer in another state, billing GSTIN to be considered as the place of supply. This would become an inter-State transaction and will be liable under IGST.
In case you have already charged CGST + SGST on earlier completed transactions, you need not make any changes in returns as section 19 of IGST Act r/w section 77 of CGST Act provide that interest would not apply, and payment of correct tax and refund of incorrect tax paid would be required only if proper officer creates an order for the same. Suo-moto changes not required.
Going forward ensure correct tax is charged to avoid issues during transfer and EWB.