Intro
Historically speaking, Muslims have believed in the “substitution-theory” since the earliest records of Islam.  Allah told Muslims that the true story of Esa (as) was actually in existence, there were some fringe heretical-christians who believed exactly that.  Todd Lawson discusses them in his book also.  It’s called docetism, these christians believed that Jesus was never on any cross, they believe it was a ghost or an image that was crucified instead or someone else (see Lawson, page 3).  There are other beliefs that differed from mainstream Christianity, like the idea that Esa (As) spoke in the cradle and that he fashioned birds and breathed life into them, all of these beliefs came from fringe Christian groups.  Never did any group of the Abrahmic religions ever belief that Jesus (as) died in India.

St. John of Damascus
This Christian man wrote a review of the new Islamic faith, you can read it here.  In terms of Jesus (as), he wrote:

“””He says that there is one God, creator of all things, who has neither been begotten nor has begotten. [102] He says that the Christ is the Word of God and His Spirit, but a creature and a servant, and that He was begotten, without seed, of Mary the sister of Moses and Aaron. [103] For, he says, the Word and God and the Spirit entered into Mary and she brought forth Jesus, who was a prophet and servant of God. And he says that the Jews wanted to crucify Him in violation of the law, and that they seized His shadow and crucified this. But the Christ Himself was not crucified, he says, nor did He die, for God out of His love for Him took Him to Himself into heaven. [104] And he says this, that when the Christ had ascended into heaven God asked Him: ‘O Jesus, didst thou say: “I am the Son of God and God”?’ And Jesus, he says, answered: ‘Be merciful to me, Lord. Thou knowest that I did not say this and that I did not scorn to be thy servant. But sinful men have written that I made this statement, and they have lied about me and have fallen into error.’ And God answered and said to Him: ‘I know that thou didst not say this word.” [105] There are many other extraordinary and quite ridiculous things in this book which he boasts was sent down to him from God. But when we ask: ‘And who is there to testify that God gave him the book? And which of the prophets foretold that such a prophet would rise up?’—they are at a loss. And we remark that Moses received the Law on Mount Sinai, with God appearing in the sight of all the people in cloud, and fire, and darkness, and storm. And we say that all the Prophets from Moses on down foretold the coming of Christ and how Christ God (and incarnate Son of God) was to come and to be crucified and die and rise again, and how He was to be the judge of the living and dead. Then, when we say: ‘How is it that this prophet of yours did not come in the same way, with others bearing witness to him? And how is it that God did not in your presence present this man with the book to which you refer, even as He gave the Law to Moses, with the people looking on and the mountain smoking, so that you, too, might have certainty?’—they answer that God does as He pleases. ‘This,’ we say, ‘We know, but we are asking how the book came down to your prophet.’ Then they reply that the book came down to him while he was asleep. Then we jokingly say to them that, as long as he received the book in his sleep and did not actually sense the operation, then the popular adage applies to him (which runs: You’re spinning me dreams.) [106]”””

Conclusions
Obviously, all the Tafsirs on the Quran and oral-tradition in the early-to-mid 700’s stated that Esa (as) didnt die…instead it was only made to appear as such….this historical document from a neutral source debunks all the lies of Ahmadiyya.  Muslims always believed that Esa (as) was never even on any cross, he escaped and Allah raised Esa (as) to heaven.