The general situation in Ireland can be condensed as follows:
Due to the peace agreements, there are two joint "prime ministers" for Northern Ireland, one of them Unionist and the other Nationalist. But the former Unionist PM, Arlene Foster, was involved in a political scandal.
As Foster did not resign on her own the Nationalist PM, Martin McGuinness, did resign, and the Sinn Fein did not present another candidate until some demands were met (including Foster being removed from her position until the scandal was properly researched). Since the agreements by which UK gave powers to the North Ireland government stablished the need of both PM, in the absence of one of them the North Ireland government became inoperative.
There are currently talks trying to unlock this situation, and this is what the comments are related to. Your second link includes the following:
The parties in Northern Ireland will meet tomorrow to resume talks aimed at restoring the devolved Stormont government. Britain is supposed to act as a non-partisan arbitrator, bringing all parties together, including Sinn Fein, the SDLP and the Alliance party.
and:
For some time now the Conservative Government, under both David Cameron and Theresa May, have not been sufficiently non-partisan and neutral on the Northern Ireland peace process, but any collaboration with the DUP could derail it entirely
So, the DUP supporting Theresa May (and Theresa May needing the continued support of the DUP to staty in power) at the very least cast a doubt about the neutrality of the UK government as a mediator. Possibilities (non exclusive):
Any proposal coming from the UK Government becomes (even more) suspect to the Nationalists.
The UK Government may effectively end supporting the position of the DUP to avoid losing their support in London, effectively ceasing to be a mediator to become a part.
Knowing that they have a great leverage on the UK Government, the DUP decides to sabotage the talks in the hope that, in case of a crisis developing and political changes being needed, the UK Government will side with their interests.
In any case, I do not see any reference to violence in either of your links, and nobody seems to be talking about that possibility. The immediate danger is the collapse of the talks for the restablishment of NI government.
There is always some risk of violence in these situations, but I would not expect it to be a direct, short-term consequence of a DUP-Conservative coalition.
The main such risk would be in the long term, if the UK Government sided completely with the DUP to the point that the Nationalists become convinced that the peace agreements have been breached. But that would require a long-term, long chain of "what if".
