In an interesting twist of events, Portuguese were actually expecting, or at least hoping, to find Christians in India. Since at least King Joao II (and probably earlier) Portuguese have been searching for the legendary Christian kingdom of Prester John, placing its location variously in the interior of Africa, in far parts of Asia, or sometimes in India. Their captains and explorers having instructions to seek out the kingdom, or at least information of it, and try to establish contact and then alliance.
This 'search' culminated with the most bemusing confusion where Vasco Da Gama in his first expedition to India had managed to misidentify the Hindu religion he found there as Christianity!
The misunderstanding first arose as Da Gama reached East African Swahili cities of Mozambique, Mombasa and Melindi. There they communicated with the local Muslim elite through Arabic translators and probably were quick to assume and mistranslate that the non-Muslims the locals talked about must be Christians. The was further complicated with mentions of the actual Christian kingdom of Abyssinia/Ethiopia existing nearby, and with numerous non-Muslim and certainly, non-Arabic traders and ships found in ports and harbors. For example, there were four ships in Melinde that Portuguese identified as being Christian Indian. They were most likely either Gujarati Banyan or from Malabar Cranganore, and if the latter is true they could just as well actually have some of the St. Thomas Christians onboard.
Whatever the case, Vasco Da Gama became certain that India was Christian so much that when he reached Calicut, a Hindu city-state in Malabar coast, he was quick to pronounce Hindi as Christians. From the journal of the voyage you can read the interesting account of the Portuguese embassy attending a Hindu temple while firmly believing they are attending some Christian ceremony, thinking images showing Hindi deities are of Christians saints, Virgin Mary, Holy Spirit etc. Vasco Da Gama continued to his audience with the Zamorin of Calicut, thinking of him and addressing him as Christian. The mistake seems not to have been corrected or recognized until the fleet returned to Portugal, as the initial letters following the return to Portugal are jubilantly talking of mighty Christians of India. But after the debrief of a captured Jew (soon to convert and take the name Gaspar Da Gama) Europeans became aware that the Hindi were not Chrisitans at all, but despite that, there was, in fact, a small number of Christians in India- which almost certainly means to the St. Thomas Christians. We don't know how much accurate information Portuguese received about this group of Christians at that point, nor how were their initial reactions to this second hand information.
Direct contact with the St. Thomas Christians came as early as the second expedition to India, under Pedro Alvares Cabral. The mission was most famous for the lucky discovery of Brazil, but other than that it was marred with many misfortunes. Five of the 13 ships were lost in the Atlantic ocean on the outgoing voyage, and in Calicut (in no small part due to Portuguese crudeness, religious exclusivity and overall sense of entitlement) the relationship with locals deteriorated quickly, culminating with the local mob attacking and killing around 50 Portuguese men onshore, to which Portuguese retaliated by burning ships in harbor and bombarding the city. Following this outbreak of hostilities, the Portuguese moved to Cochin, where there was a small Christian community of St. Thomas, which might be the reason they chose to go to Cochin in the first place. There, two priests from the local Christian community expressed the desire to return with Portuguese to Europe to visit Rome, Jerusalem, and then to reach their bishop in Syria. Unfortunately, one of the priests died on route, but the other, Priest Joseph reached Portugal, and then Rome and Venice before proceeding to Jerusalem. During the stay in Italy, he was interviewed and the summed up account was printed and published as early as 1505, familiarizing Europe with some of the details of Christians in India. You can find the account here.
The above is more or less an account of the proceedings of the first contacts, but with little analysis of reaction by the Portuguese. As was attempted to demonstrate, the Portuguese weren't surprised to find Christians in India. If anything they turned out to be disappointed that there are less of them than first assumed. The authenticity of St. Thomas tomb was accepted without question, and it became a popular pilgrim site for Portuguese in India, as it already was for Indian Christians. Portuguese were quick to connect with fellow Christians, no matter how different they were, as they were also eager to establish a link with the Ethiopian kingdom, because they tried to seek allies against the Moors and gain allies.
The closest we have to the official reaction on St. Thomas Christians is the excerpt from the letter of King Manuel to Castillian monarchs following the Cabral expedition is. Here it is quoted:
In that kingdom there are many true Christians of the conversion of Saint Thomas, and their priests follow the manner of life of the apostles with much strictness, having nothing of their own except what is given them as alms. And they practise celibacy, and have churches in which they say mass, and they consecrate unleavened bread, and wine which they make from dried fruit with water, for they cannot make other. In their churches they have no images save the cross, and all the Christians wear the apostolic garments, and never cut their beards and hair. And there he found definite information concerning where the body of Saint Thomas lies, which is 150 leagues from there, on the sea coast, in a city which is called Maliapor [Mailapur], of a small population; and he brought me earth from his tomb. And all the Christians and also the Moors and Gentiles, on account of the great miracles which are performed, go to his house on pilgrimage. He also brought us two Christians who came of their own accord and with the permission of their prelate, so that we might send them to Rome and to Jerusalem, to see the things of the Church there, and to be informed about them, for they consider that they are better ruled by being ordained by Saint Peter, who, they believe, was the chief of the apostles.
Despite soon to be obvious differences in religious observance, Portuguese seems to in the first few decades not place much effort to change but hoped this would occur naturally. when this, in fact, didn't happen naturally, it became a major issue in the second half of sixteenth century when - galvanized by counter-reformation - Portuguese clergy was trying to force those communities into the Catholic teaching. The effect was, naturally, distancing and resentment of those communities from the Portuguese and Catholic faith, but this is another, far more complicated topic on which I am less competent to talk about.