I think Jats are not called Indo Iranians as they are living across the Indus for a lot longer, and speak Indic languages. In the rural areas of Punjab even the kakkay zais speak Punjabi now. I do not see Punjabi as a race, anyone living in Punjab is a Punjabi. Multiculturalism being propagated in the world these days has been practiced in Punjab and Sindh through out history.
This is the crux (regarding Jats) that I gathered from Ahmed Dani’s book on Pakistan’s history: