I suspect you may be following a mistaken path - the Manx name Cain is very common - it was often writen as Kane in 19th century (sometimes I think to avoid the Biblical analogy) and also as Caine (possibly for similar reasons though boith Kane and Caine are actually early forms) - however Caines was not a manx variant - it occurs just once in the 1881 census (and that is someone on board a vessel) - it never appears in any of the many 19th century directories on my site or in any other context except once or twice when Family historians talk about multiple John 'Caine's as did J H in the page you obviously found via a web search.
eg history on Isle of Man is:
CAIN, or CAINE, contracted from Mac Cathain, ' Cathan's son.' This name may be rendered 'warrior' (cath 'a battle.')

The O'CATHAINS, now O'KANES, were of the race of Eoghan, who was son of Niall of the Nine Hostages, Monarch of Ireland, who died A.D. 4o06.
The race of EOGHAN of valiant arms,
Who have obtained the palm for greatness without fraud,
The acme of the nobility of Erin.'*

EOGHAN UA CATHAIN, abbot . . . died,' A.D. 980+

Compare (Irish) KANE and O'KANE.

McKANE [1408], MAC CANN [1430], MAC CANE [1511], CAIN [1586], CANE [1601], CAINE [1609], CAYNE [1610].