I didn't get anywhere with Miller either.
Looked at Historical Directories and I am even more confused that before.
The 1911 census gives James Tuppen living at 1 North St Eastbourne and a confectioner with his wife as an assistant, there are the two children and a lodger Frank Saunders, a whitesmith. No other people are listed. In Kelleys directories for 1911 and 1915 a John Tuppen is listed at 1 North St Eastbourne as a confectioner but a John doesn't appear in the census.