If all indo european languages come from one language, does that mean that it used to be one people who spoke that language?

Probably, but not necessarily. As the astute Joachim Pense put it (answering this question, rather than the OP’s question):

Joachim Pense’s answer to Linguists believe Proto indo European is the root of all those European languages. Does this mean that at one time everyone spoke the same language?

No. Proto-Indo-European is a reconstruction that has a scope of many centuries and a large area. The reconstruction is not able to get to a finer resolution.

In fact, the idea has been put out there (by Trubetzkoy) that Indo-European may not have been a single language at all, but a Sprachbund of languages. The reconstruction assumes that it was a single language, but the reconstruction does that for methodological reasons: it’s not like we actually know.

Even if Indo-European was a single people, languages are not genetically transmitted. There’s a lot of genetic diversity in people who speak Indo-European languages now; there may have been some diversity back then too—especially if Indo-European was always a language that spread from place to place, whether culturally or militarily.