I have my iPhone located with me in America and iPad which is in India. Recently, one of my family members logged in to iPad using my iCloud account, so did my iMessages also get synced to that device automatically?
Maybe. Maybe not. If iMessage is configured with the same Apple ID on both devices AND that Apple ID is used for sending and receiving iMessages then whatever messages you sent and received will be displayed on both devices as long as they are connected to the internet.