I can't see the marriage, but I thought it was worth looking for Martha Hinkin and found this:
Marriages December 1884
HINKIN Edwin Thomas Llanelly 11a 1325
JAMES Martha Llanelly 11a 1325
In 1891
Great Western Terrace, Llanelly
Edwin T Hinkin head 28 Tin man Iron works Glamorgan, Ystabyfera [?]
*Margretta Hinkin wife 26 Glamorgan, Mountain Ash
Miriam G Hinkin daur 3 Llangennech
Robert H Hinkin son 1 Llangennech
Evelyn G S Hinkin daur 7m Llangennech
Census ref:Class: RG12/ Piece: 4493/ Folio 114/ Page 32
*Image does read Margretta, but bear with me, I think she's Martha.
1881 census
"adjoining York Hotel" Llanelly
Margaret James head W 45 Charwoman Tredgroves, Cardigan
Elizabeth James daur 18 working in tin works Maesteg, Glamorgan
Martha James daur 16 working in pottery Mountain Ash, Glamorgan
Margaret James daur 11 At school Mountain Ash, Glamorgan
Marim James daur 9 At School Mountain Ash, Glamorgan
Census ref:Class: RG11/ Piece: 5373/ Folio: 114/ Page: 5
So, considering the possibilty that Martha Hinkin is Elizabeth James/Tyler's sister, a search of the 1891 census for Elizabeth born in Maesteg c1863 shows up only one who is in Carmarthenshire:
Household of Thomas Thomas at 10 Bay View Terrace
Elizabeth Taylor servant M 19 General Servant Maesteg, Glam
Can't see the Hinkin family in 1901 - although there is a probable marriage of one of the daughters in Pontypridd district in 1912, and Robert H Hinkin died in Llanelly district in 1963.
Edwin James Tyler isn't showing in 1891 - he isn't with (possible) grandmother Margaret James [Census ref:Class: RG12/ Piece: 4495/ Folio 75/ Page 27]