It's interesting that lots of notable 19th century nationalist leaders were from Protestant or Anglo-Irish backgrounds - Charles Stewart Parnell, Douglas Hyde, WB Yeats, Lady Gregory, etc - but, as you say, people of these backgrounds became much more concentrated in north-east Ulster by the second decade of the 20th century, and onwards.
This also won’t be the best answer you’ll get but I can provide some very general contextual information which hopefully will be helpful; there are a lot of factors involved and I’m by no means an expert on most of them!
One clarification: I generalise and discuss Protestants as a whole - including Church of Ireland, Presbyterian, Methodist - to paint a broader picture. I hope this still manages to answer your question, even though you have specified Presbyterians. It’s also important to note that the direct correlation between religion and political affiliation intensified in the twentieth century to the extent that by the onset of the Troubles (late 1960s), Catholic = Nationalist and Protestant = Unionist. In the 19th century, for example in the Gaelic League, it was common to be Anglo-Irish and also to promote Irish language and culture, so the dichotomy was less severe.
Partition is central to this. In the 17th century, the Plantation of Ulster created an Ulster Protestant community in the north which endured and resulted in economic and migratory ties with Britain and a higher proportion of Protestants, particularly in the north-east. This meant that going into the 20th century Ulster (specifically the 6 Counties) had a decidedly more “British” character than somewhere like Cork, for example. In May 1921, Ireland was formally partitioned under the Government of Ireland Act of 1920 along these differences and, loosely, boundaries.
In the south: following independence in 1922, the new Irish Free State effectively became a Catholic state. There was no separation between church and state and Catholic values were enshrined in the 1937 Constitution. There were plenty of Unionists in the south but this move towards establishing a “Catholic” Ireland plus the fact that they had been targeted throughout the War of Independence and Civil War led to their gradual emigration, mostly to Britain as far as I know but presumably to Northern Ireland too. Lots of work has been done recently on Ireland’s Southern Loyalists - they weren’t all forced out but they certainly were not made welcome. The percentage of Protestants and Catholics in the 26 counties changed rapidly and you can see how the south became an even more overwhelmingly Catholic country - the Central Statistics Office has a handy chart here.
At the same time, the North remained more mixed - Catholics and Protestants comprised approx 30-40% each of the population throughout the 20th century - I found this document on the 2011 census.
A major effect of this Catholic emphasis in the Free State, violence during the revolutionary era, and the higher percentage of fellow Protestants in the north was the alienation of Irish Protestants in the south - they no longer fitted into the image of “Ireland” and what the new Free State government hoped to achieve. Large numbers of them left and those that remained no longer identified with or felt a part of the nationalist movement and its vision for an independent Ireland, nor were they seen as a part of it.
In the new Northern Irish state then, there were nationalists (the majority of whom were Catholic) who felt abandoned by the leadership in Dublin and unionists (majority Protestant); these groups were already in violent conflict by 1920-22 and they became more polarised throughout the 20th century. Loyalties in Northern Ireland are hugely significant but because I’m less familiar with the complexities of the later 20th and 21st century history, I wouldn’t be able to do it justice here.
But hopefully this general information on the later 19th century into the revolutionary period provides some useful background information and context. In brief: Ireland's nationalist movement came to be a more Catholic and anti-British one and Irish Protestants were at odds with it.
On southern unionism:
For Ulster Unionism see anything by Alvin Jackson, his list of publications is here.