No such thing as a special visa.
Non nationals living and working in Ireland with a work permit have a number of obligations. Once they receive the work permit, they must register with these people http://www.inis.gov.ie/ who will then give them "permission to remain" in Ireland. This takes the form of a stamp in their passport, and an Immigration card. it is valid until the end of their work permit.
If they wish to leave the country an re-enter (for whatever reason holiday, work abroad, trip "home") they must have a re-entry visa given to them by the same people. All re-entry visas are issued until the date of their permission to remain expires. Most non nationals living in Dublin get their Immigrattion stamp and visa sorted on the same day. If he had a 2 year work permit (which is possible after initial one year is issued), then the immigration authorities would not have any dealings with him.
Before his first job he'd apply for PPS number (He'd need to show work permit, immigration stuff etc). As long as tax is beeing paid on each employmee, that Department would not be alerted to where the employee is from, or what his status is. its all just fed into a system.
Joseph would've needed a Schengen visa issued to him to play in Austria but as long as he had his Irish immigration details as above, that wouldn't have been a problem