My understanding is that the initial Yamnaya advance is regarded as quick; a couple-three hundred years to from the steppes to the Atlantic. The language splits come with the transition to the bronze age and if not new populations then definitely new political centres and cultural traditions. (But are fundamentally lurking in misty pre-history and there's an awful lot we don't know about back there, e.g. the remnants of the big neolithic battle where everyone would have thought there couldn't be enough people for a battle.)