NI tax liability for ROI PAYE earnings

My wife is working in Dublin but living in Belfast.
I had (mistakenly) thought that she would pay tax in ROI and not file for taxes in NI.
As I understand it she must file a return in NI. She can claim married tax credits in ROI but will have to pay the difference to HMRC if her tax liability is less than for NI.
Does anyone know what the date is for filing a Tax return in NI? and is PRSI considered a tax?
All pointers gratefully received
Thanks,
Harpz

Also: does it make a difference if the money earned stays in ROI? i.e. not trasferred to NI

Is her employer NI or ROI, or is she self employed.

Her employer is a University.
She is a PAYE employee.
AFAIK employers in the ROI are counted as UK employers by HMRC but working in ROI counts as working overssees.
I think I came across something about employees of the state not having to pay NI taxes...Is this the case? and does an employee of a University (funded by the Irish Government) qualify.
Any/all further information welcome.
Thanks,
Harpz