How is it possible for the lands including the "-stans" to still speak Indo-European languages, as in the ones they spoke before the Turks rolled through?
It is fine if there are Turkish minoritys in Central Asia and if the land is dominated by a foreign power. Preferably with a POD after 800 AD.
I don't think all of Central Asia can be Indo-European-speaking, and I doubt it ever was.
The northern parts of Central Asia (e.g. Kazakhstan and Kyrgyzstan) were never really dominated by Indo-European-speakers, not even in ancient times.
The southern parts of Central Asia (e.g. Afghanistan and Tajikistan) are still Indo-European-speaking until this very day, so your question shouldn't apply to them.
It's the core that kept changing (e.g. Turkmenistan and Uzbekistan). However, do bear in mind that the overwhelming majority of modern day Turkic-speaking Central Asians, especially the people of Turkmenistan and Uzbekistan, predominantly descend from ancient Caucasoid/Iranian populations. Around 70-80% of the Turkmen DNA haplogroups derive from Caucasoid/Iranian populations, and around 60% of the Uzbek DNA haplogroups derive from Caucasoid/Iranian populations. The remaining 20-40% haplogroups come from other origins, notably Northern Mongoloid (Siberian) populations, most of which are from female lineages, ironically.
So the Central Asians are practically the same people, but they underwent language shifts according to the geopolitical situations. This is attributed to the fact that many urban dwellers went back to nomadic lifestyles and therefore adopted the language of the nomads, which was in most cases Turkic.
However, you might find this hard to believe but Indo-European languages, especially Persian, still dominated Central Asia up until the 19th century. In terms of language dominance, it was only after the Russian colonization of Central Asia that Persian began to lose its status as the official language of country in the "Turkic" parts of Central Asia, thanks to Russian initiatives.
So for Persian to continue being spoken as an official language in most Central Asian countries, the Russians should have lost the Great Game. The British were no better either. They ended the dominance of Persian in India and replaced it with English. The Russians ended the dominance of Persian in most of Central Asia and replaced it with their own language as well. Kazakhstan and Kyrgyzstan today are Russianized and set to join the Eurasian Union.
Uzbekistan is the only country lost in the middle. It wants to neither join the Russian sphere nor Persian sphere. Yet the irony is that almost half of the country is Tajik, all the ministers are Tajik and their language is heavily influenced by Persian.
So has anything really changed? Not really if you think about it. The Eurasian heartland was always a complicated place. It's the homeland of all Eurasiatic language families, including Indo-European and Turkic.