Wikipedia states:-
"The tune is that of an old Welsh air, first found in a musical manuscript by Welsh harpist John Parry Ddall (c. 1710–1782), but undoubtedly much older than that. The composition is still popular as a dance tune in Wales, and was published in the 1784 and 1794 editions of the harpist Edward Jones's Musical and Poetical Relics of the Welsh Bards. Poet John Ceiriog Hughes wrote the first published lyrics for the piece in Welsh, titling it "Nos Galan" ("New Year's Eve")"
Wikipedia continues:-
"Charles Wood arranged a version, the words from Talhaiarn; translated by T. Oliphant. Oliphant died in 1873 and the first English version of 1881 is attributed to him."
Talhaiarn (John Jones) and Oliphant worked closely on many works including: "Welsh Melodies, with Welsh and English poetry", by J. Jones (Talhaiarn) and T. Oliphant. I have not checked this publication altough Deck the Hall with Boughs of Holly is said to be in it:-
"WORDS AND TUNES FROM THE BEST POETS AND MUSICIANS SELECTED AND ARRANGED BY JOHN HULLAH 1884" states:"Words (translated from Talhaiarn) by Oliphant. TUNE New Year's Eve. From Thomas's Welsh Melodies"
There are four volumes to "Welsh Melodies". The first two were published in 1862, the third in 1870, fourth 1874.
If Deck the Halls is in "Welsh Melodies" then it not only confirms Thomas Oliphant as the author of the English Version (which is clearly not a translation of the Welsh) but it would also pre-date the 1881 publication which attributes it to Thomas Oliphant anyway.