There is no parish of Newmill, that's a placename in Auchterless parish.
From the 1881 census of Auchterless, John Milton age 53 from New Deer parish, a married farm servant, is away from his family working at Seggat. His wife Margaret, a farm servant's wife from Auchindoir parish, is with their children at a "house on Darley".
But, in 1871 this same John Milton, with his family at Seggat, Auchterless, claims to be born in Aberdour parish.
In 1861, Ancestry has mistranscribed Margaret "Wilson" from Auchindoir at Templand, Auchterless with 1yr-old son William. John Milton age 28 is at a separate household at Templand and is said to be born in Forgue parish. This may be a "Ditto" from the previous entry. The original record can be viewed on Scotlandspeople. NEVER trust Ancestry transcriptions.
In 1851 John (cattleman age 21) appears to be working in Turriff parish, born in Aberdour parish. [Freecen.org.uk]
In 1841 John Milton is at New Mill, Auchterless age 13 born Aberdeenshire, with his grandfather.
So, it seems that John was not entirely sure where he was born, but Aberdour and New Deer are the favourites.