Tumbleson is simply another way of spelling Tomlinson. Such variations are very common in Ireland. Kirkpatrick/Kilpatrick, Falconer/Faulkner, Robertson/Robinson, Nogher/Connor, Patterson/Pattison, , McConnell/McDonnell, Kerr/ Carr, Stewart/Stuart are other examples.
The idea of a single or correct spelling for a surname or a place name in Ireland is very much a recent phenomenon designed to meet the needs of modern officialdom. Before that there was no consistency. Names were spelled phonetically and each variation was down to the whim of the particular person recording the information. You will often see the spelling change as the records go back. This rarely indicates a deliberate decision to alter the name, nor even a mistake. Not everyone was literate, but even when they were, exact and consistent spelling simply wasn’t something they bothered about. In addition to varying the actual spelling, O’ or Mac prefixes were optional and were often omitted.
In 1899, the Rev Smith reviewed the early records of Antrim 1st Presbyterian church (covering the years 1674 to c 1736). He noted: “Even the same word is not always spelled alike by the same hand. Indeed spelling with most of the recording officials (and they must have been fairly numerous) was a matter of the most sublime indifference. The name William, for instance, is spelled 3 different ways in as many lines; while Donegore, a neighbouring parish, is spelled 10 different ways; but these extend over a good number of years. Many families names are spelled phonetically, while others are given in the most round-about fashion.”
So expect spelling to vary. That was the norm.
This looks to be the family in the 1901 census. Different spelling again.
http://www.census.nationalarchives.ie/pages/1901/Antrim/Seacon/Ballinacree_Skein/942266/
Family in 1911:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Seacon/Ballynac…
Son James birth certificate:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1881/02808/2030251.pdf
Tradition was to marry in the bride’s church so Drumreagh Presbyterian may be where Margaret Jane Cooper was baptised. That churches records start in 1864 for baptisms and 1845 for marriages. Copy in PRONI in Belfast.
This is probably Hugh Cooper’s death in 1908. Wife Margaret Jane still alive:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1908/05498/4540061.pdf
Margaret Jane in 1911:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Seacon/Ballinamore_Town/126640/
Hugh’s marriage to Margaret Jane Thompson in 1878:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1878/11106/8065056.pdf
Birth of Margaret Jane Cooper in 1884:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1884/02705/1995935.pdf
Anna looks to have been born 6th Feb 1882.