Children born in New Zealand appears he was there from about 1879 to about 1888 then returned to England and then in 1890 he went to NSW.
1881/13273 Chaffers-Welsh Cyril Gerrase Helena Baker Jeremiah -
1885/4842 Chaffers-Welsh Agnes Eirene Helena Baker Jeremiah -
1883/17113 Chaffers Welsh Muriel Katharine Helena Baker Jeremiah -
1880/18998 Chaffers-Welsh Constance Mary Geraldine Helena Baker Jeremiah
1887/13926 Welsh John Theodore Helena Baker Chaffers Jeremiah Chaffers
Auckland Star, Volume XIX, Issue 176, 27 July 1888, Page 2
Departure of the Aorangi. Lyttelton, Thursday. Sailed S.S- Aorangi, for London, via Rio de Janeiro.
..........Second Saloon.......extract.......Rev. J Chaffers, Welsh, Mesdames Helen and Ruth Welsh, Misses Geraldine, Muriel le and Agnes Welsh, Masters Cyril and John Welsh.............
Otago Daily Times , Issue 8912, 17 September 1890, Page 4
The Rev. Chaffers Welsh, late of Christchurch, has been appointed domestic chaplain to the Bishop of Sydney, and will sail for New South Wales on the 15th. He was educated at St. Aidan's College, Birkenhead, and was one of Dr Saumarez Smith's earliest students.
As for the name change I think it appears that it sounded more official and important and often was assumed that his surname was Chaffers Welsh. With some papers adding a hyphen and others not.