Sometime between 1861 and 1871 it appears that most of the Warne family left Cornwall and moved to Wales. They were lead miners.
On the 1871 census Elizabeth (now a widow) is living in the village of Coedpoeth, to the west of Wrexham. Her husband John presumably died in Cornwall.
Living with her are married son James and single Samuel. Another son, is married and with three children (all born in Cornwall).
Elizabeth died in Coedpoeth in 1880.
James had left Cornwall between 1851 and 1861 and had moved to Carmarthen, Wales and married there. He had moved to Coedpoeth by 1871 (but his family were still in Carmarthen) and remained in Coedpoeth, where he died in 1895.
John also remained in Coedpoeth, where he died in 1895.
Samuel married Mary Williams in Wrexham in 1874 and, by 1881, they were living in Midlothian, Scotland.
Emanuel appears in the 1861 census in County Durham, England.
The other son, Francis, "possibly" emigrated to Australia???
But, unfortunately, you are not going to find Josiah in Wales! On the 1861 Census he was living in Cornwall but in 1869 he married in Manhattan, NYC, USA. So if he did live in Coedpoeth it was between censuses.
There are several Warnes still living in Wrexham today.
I've no idea why they would have lived in Trallong in Breconshire, Wales though. As it's on the edge of the Beacons there may have been some lead mines in that area but I'm not aware of any? If they did live there then, again, it must have been briefly and between censuses? I can't find the photo on your site.
Which person is it attached to? Is it the postcard of a lake below a range of mountains attached to several people in your tree??? If so, this is most definitely NOT Cornwall, not even Britain! It's Alpine, more likely to be Switzerland, Austria, southern Germany, northern Italy ....