Hi, it is not clear to me whether after two years in a J-1 as Visiting Professor in academia, I am obliged to not only pay the taxes as expected, but also to give back the unpaid taxes for the first two years, as it is customary for Germans or Indians. It was not like that with the old tax treaty of 1985. I am not sure about this new tax treaty. Thanks.

There is no such clause that you have to refund the taxes back if your stay exceeds 2 years. Read IRS publication 901.

Agreed; there is NO retroactive tax clause in the Italian treaty.