Some of what Achaya has to say about the potato's history in India is reproduced below, including his references. He may well be wrong, or may simply have presented only one side of a controversial issue. I think most accounts of the potato in India assume Fryer (see below) witnessed the potato, not the sweet potato.
Though termed papa in South America, they [potatoes] were incorrectly called batata (the name for the sweet potato) when John Gerard first described them in English in 1597, and this name stuck. As a result of this confusion in nomenclature, it is doubtful whether the potato mentioned in the well-documented dinner given in Ajmer by Asaf Khan to Sir Thomas Roe in 1615  and again noted by Fryer in 1675 as constituting a garden crop (along with the brinjal) in Karnataka and Surat, was really the potato at all, and was perhaps the sweet potato, known much earlier in India. [32d, 320].
However, the identity of the 'basket of potatoes', considered worthy enough to be offered as a gift to Warren Hastings around AD 1780, is not in doubt, since he even invited members of his Council to dine with him and partake of the unusual gift [32d].
...By 1780, potatoes, peas and beans, according to an 1860 report , were in high repute as foods in Calcutta; the report adds that 'the Dutch are said to have been the first to introduce the culture of potatoes, which were received from their settlement in the Cape of Good Hope. From them the British received annually the seeds of every kind of vegetable useful at the table, as well as several plants of which there appears to be much need, especially various kinds of pot herbs.' 
..In about AD 1830, potatoes came to be grown on terraced slopes in the Dehra Dun hils though the efforts of a Captain Youns and a Mr Shore who simultaneously developed the hill stations of Mussoorie and Landour. 
..at first it grew especially well in elevated terrain. A major breakthrough in the control of viruses spread by aphids enabled very high yields of potatoes even in the plains.
Elsewhere, Achaya writes:
In AD 1615 Edward Terry mentioned potatoes, and so did John Fryer in AD 1678, but since potatoes had not by then reached India, these were probably sweet potatoes, which were equally strange to the English visitors.
[32d] J.B Hutchinson (ed.) Diversity and Change in the Indian Subcontinent, Cambridge University Press, 1974, M.N. Upadhya, p. 139
 Mohommad Azhar Ansari, European Travellers under the Mughals (1580-1627), Idarah-i-Adabiyat-i Delhi, Delhi, pp. 76-103
H.A. Jones and L.K. Mann, Onion and its Allies, Leonard Hill Books Ltd., London, 1963, p. 18 and p. 36
Pushkarnath, The Potato in India, Indian Council of Agricultural Research, New Delhi, 1964.
Ruskin Bond, 'How Potato Spawned a Hill Station', Sunday Herald, Bangalore, 18 January 1987.
James Long (ed.) 'The Adventurers', Calcutta Review, 1860, vol. 35; reproduced in Echoes of Old Calcutta, S. Das Gupta (ed.), Naya Prakash, Calcutta, 1981, pp. 68-138.
B.B. Nagaich, 'Major Achievements in Potato Production through Plant-protection Research', Golden Jubilee Symposium, Indian Council of Agricultural Research, New Delhi, Sept. 1979.
Elsewhere one finds that the potato was introduced into England in 1590. India recently overtook the US to become the third largest producer of potatoes, behind China and Russia.
Avars, Arabs, and History
41 minutes ago