I think your RCIA instructor is a little off or maybe just somewhat unclear on this matter. The first Vatican Council in the late 19th century affirmed the infallibility of certain Papal Pronouncements and defined the conditions under which a pronouncement was to be considered infallible. There were some at the Council who would have made the definition less restrictive but their position did not fly. The Popes have the charism of Infallibility in matters of faith and morals since Peter became the first Pope. It was not an invention of the 19th century.
Vatican II affirmed that the Bishops gathered in Council with the Pope were infallible with probably the same restrictions.
That does not mean that certain matters of faith and Morals proclaimed before those two Councils were not infallible. Decisions made by Ecumenical Councils, of which there now have been 21, which were then affirmed by the Pope were infallible. Encyclical letters written by Popes down through the ages may contain infallible material, but are not in themselves considered infallible unless the Pope meets those conditions laid down at Vatican I.