By "British descent" he means that they would be the descendants of the English and Scottish people who were transplanted into Ireland in the 16th and 17th centuries in order to "Anglicise" the Irish natives who were continuously rebelling against English (and then British) rule.
The Ulster Plantations were the only ones that were actually "successful", mainly due to the other plantations either: giving out too much land to a planter, or not enough people actually wanting to go.
When Ireland got its independence, most of the "unionists" (i.e people wanting to stay in the UK), basically moved there, to allow them to continue living in the United Kingdom. This created a pretty shitty situation for the nationalists who were ruled in the words of Unionist, Lord Craigavon, by a "a Protestant parliament for a Protestant people".
The resulting discrimination of the Catholic (/nationalist) community was a driving cause for the beginning of the Troubles which rapidly spun out of control with horrific actions committed by all sides.
Also, not that I care about it too much, however the name "Southern Ireland" is disingenuous to use in the context of the independent part of Ireland (i.e Republic of Ireland), as it was the name of a state that was still part of the United Kingdom during its existence.
While it may be the simplest name for some, Ireland, Éire (while speaking Irish) or the Republic of Ireland are generally the names that should be used to refer to my country (I understand people dislike using a name that sort of claims the entire island).
End note:
I want to end this by saying, while it may seem I'm taking this from a biased side, I don't support what is, to be honest, a blatant attempt to stir shit up. If they wanted it up legitimately they could have went through all the necessary negotiations to get an agreement that would have allowed this to happen.
While I do support a so-called "United Ireland", it should be one where all sides are respected and treated with respect, the lessons of what happened in Northern Ireland show us this.