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Sorry Maciamo, I'm afraid that really makes no sense. Where would the Tocharians come from if they only arrived in the 3rd century AD? No matter which hypothesis you prefer in regard for the affiliation of the Tocharian language, it's clear that the language must be pretty ancient, and 2000 BC is indeed a likely date for the arrival. In my opinion, the Tocharians were indeed R1a, and M73 is a Haplogroup of the Uighurs/Turkic peoples.
Tocharian speakers could have arrived from somewhere else in Central Asia (Turkmenistan seems to have a lot of unexplained R1b-M73) or even from Siberia, as descendants of the Afanasevo culture which was founded by immigrants from the Don-Volga region circa 3600 BCE according to David Anthony (old enough to still be Centum).
I also don't think that there were Indo-Iranic peoples in the Tarim basin. Mind you, before the discovery of the Tocharian inscriptions, nobody even suspected Indo-Europeans to have lived there.
There is so much we don't know and may never know. However it is pretty clear that the only Indo-European expansion in Central Asia was that of the (Proto-)Indo-Iranian of the Andronovo horizon. It spread all along the western edge of the Tian Shan, so it's not a big step to cross it to the Tarim basin. There is a passage in the Tian Shan east of Kashgar leading right into Tajikistan, a tremendous R1a hotspot. The passage was used by the Silk Road in the Middle Ages. I am pretty sure that the R1a people of the Tarim mummies came through that road from Tajikistan, as part of the Indo-Iranian expansion. That's pretty much the only way you can access the Tarim basin from Central Asia. The only other possible entry road for R1a is from the north along the Altai, through modern Karamay and Urumqi. But why would they go all this way to settle in a forsaken, mountain-locked desert oasis when they could just as well stay around Urumqi and Turpan, the population centres of modern Xinjiang ?
Note that the Tocharian script were found only in the north of the Tarim basin, while the mummies were found all along the desert, even the remote southern edge, which is best accessed from Tajikistan rather than from the Urumqi region.
Secondly, the red-haired Tarim mummies wearing tartan clothes similar to those of Hallstatt only dated from 1000 BCE, and were not tested for DNA. They might have been a later arrival to the region (who knows perhaps a very far offshoot of Hallstatt, as incredible as it sounds ? But the presence of red hair and tartan and a Centum language, all associated with Celtic people, in the Tarim basin is all incredible enough in itself, so why not ?)
It seems likely to me that the Tarim mummies were not a long continuous genetic line, but that each period had its own fresh arrivals from outside.
EDIT : from Wikipedia
"It is the Afanasevo culture to which Mallory & Mair (2000:294–296, 314–318) trace the earliest Bronze Age settlers of the Tarim and Turpan basins. The Afanasevo culture (c. 3500–2500 BCE) displays cultural and genetic connections with the Indo-European-associated cultures of the Eurasian Steppe yet predates the specifically Indo-Iranian-associated Andronovo culture (c. 2000–900 BCE) enough to isolate the Tocharian languages from Indo-Iranian linguistic innovations like satemization."
"Hemphill & Mallory (2004) confirm a second Caucasoid physical type at Alwighul (700–1 BCE) and Krorän (200 CE) different from the earlier one found at Qäwrighul (1800 BCE) and Yanbulaq (1100–500 BCE). This study confirms the assertion of Han  that the occupants of Alwighul and Krorän are not derived from proto-European steppe populations, but share closest affinities with Eastern Mediterranean populations. Further, the results demonstrate that such Eastern Mediterraneans may also be found at the urban centers of the Oxus civilization located in the north Bactrian oasis to the west."