Really, it's mind-blowing to me how Portuguese and Hindi could be related and that a Portuguese and a Indian might have come from the same people.
I mean, I know, if we go back at the beginning of human race, we all come from the same place. But isn't that TOO broad? If there's a Indo-European people/language branch it must mean there's another groups, right?
How come? How were these split?
OK, here's an important point that you need to fix on first: Proto-Indo-European, is a language, and Indo-European is how we describe languages that developed out of PIE. Neither term refers to a race or ethnicity, except indirectly. That being the case, there's no direct reason to infer that modern speakers of Indo-European languages are ethnically or genetically related to one another.
Confusion arises because of two points.
PIE was a language, or perhaps a cluster of languages, and languages need people to speak them. So there was a group living thousands of years ago who spoke Proto-Indo-European, and it only makes sense to call them Proto-Indo-Europeans. From linguistic details it's even possible to make some inferences about their environment and culture. But that's strictly the people who spoke PIE; it says nothing directly about other groups who have spoken Indo-European languages over the millennia.
Ethnicity is an important vehicle for language spread: for example, the majority of the English-speakers who live in Australia today are descended from the British and Irish, so it does make sense to think of anglophone Australia, as an ethnic group, as primarily derived from the ethnic groups of the British Isles.
But ethnicity is far from being the only vehicle for language spread. If you think of the USA, and look at the ethnic groups outlined in the 2000 census, you'll see that ethnic origins in the British Isles account for only 22.7% of the population. That's more than any other single group, to be sure, but it is a minority. A classic example for linguists is Hungarian: linguistically, Hungarian is a Ugric language, related to various languages spoken in central Asia; but genetically, the Hungarians are totally unrelated to the speakers of those other languages, and are European through and through.
The relationship between ethnicity and language is inevitably watered down over time. The exact mechanics of how the spread of the IE language group worked is an area of ongoing debate in historical linguistics. But however it happens, we can presume that initially there was a strong correlation between language and ethnicity; but that that correlation weakened, for reasons and at rates that depend on historical accident. The correlation is still strong enough that [it makes sense to conduct studies of the](http://www.jolr.ru/files/(105)jlr2013-9(23-35).pdf) relationship between language and genetics; but the results are generally pretty negative. The Proto-Indo-European language was spoken a very long time ago, and it's had a lot of time for any supposed genetic relationship between the groups you mention to get watered down into merest traces.
TL;DR: there's no need to imagine any relationship between the Portuguese and the Indians. The languages are related, but that doesn't translate into any other kind of relationship.
Try /r/linguistics!