For this sequence of events to have occurred, the Indo-Aryans would have had to have moved through the BMAC during this time period and later moved into Iran and India, not the other way around.
The language of the loans is not known, but it is apparently the language of the BMAC people.
The IA people only brought a few farming related words with them from Central Asia – the remainder were borrowed from the new locals.
40% of Hindi agricultural words still derive from an unknown pre-Munda language of the Indo-Ganges Plains.
So there is a BMAC or Central Asian substrate in Indo-Iranian.
A possible guess for the language of the BMAC people might be a relative of the Burushaski language of northern Pakistan.
The loans must have come from somewhere else, apparently the north. We have numerous references in the Vedas to battles between the Arya with their stone forts, metals, horses and chariots against the more sedentary peoples living in South Asia at the time. There are pottery shards in the BMAC that resemble that shards found in the steppe culture to the north.
It is only among Indian nationalists and a few hacks and kooks that it is not accepted. There is a substrate of a language that looks like a Munda language in the Rig Vedas.
Instead, this borrowing is precisely what we would expect to see when pastoralists from Central Asia move into the tropics, encounter new plants and animals and start farming – they borrow the terms for these new living things and technologies from the locals.
This is particularly so in the case of farming, which was left to the local people – the Sudra caste.
Nahali, a small language in Madhya Pradesh, at successively lower levels of its vocabulary, displays high levels of borrowing from earlier tongues.
36% of vocabulary is of Kurku (Munda) origin and 9% is Dravidian.