Under the 1947 Act:
33.-(1) Subject to the following provisions of this section, in this Act the expression "compulsory school age" means any age between five years and fifteen years, and accordingly a person shall be deemed to be of compulsory school age if he has attained the age of five years and has not attained the age of fifteen years and a person shall be deemed to be over compulsory school age as soon as he has attained the age of fifteen years: [...]
(2) As soon as the Ministry is satisfied that it has become practicable to raise to sixteen the upper limit of the compulsory school age, it shall lay before Parliament the draft of an Order in Council directing that the foregoing provisions of this section shall have effect as if for references therein to the age of fifteen years there were substituted references to the age of sixteen years; and if within the statutory period both Houses of Parliament resolve that the draft be presented to the Governor of Northern Ireland, the said Governor may by Order in Council direct accordingly.
110.-(1) A local education authority shall have power to make bye-laws prescribing two or more dates in each year as the dates of commencing and terminating, or otherwise in relation to, school attendance for children within their education area, and publication of the prescribed dates shall be made by advertisement or otherwise as the authority think fit.
(2) For the purposes of the provisions of this Act relating to the limits of the compulsory school age, a child shall be deemed not to have attained any particular age until the prescribed date next succeeding the date upon which he attained that age.
So it looks like the local authorities were given power to define the dates on which someone ceased to be of compulsory school age, in much the same way as they could set term dates, and there was no fixed rule. I haven't been able to find any of these announcements in the Belfast Gazette (though I may not have been looking for the right keywords...)
The limit of fifteen was postponed for a few years (it remained at fourteen until at least 1951), and was later raised to sixteen in 1972 (announcement).