Actually, it was
during the Reformation era when more explicit explanations concerning non-Catholics being saved were developed, since so many simple individuals were led astray, Calvin was denying the universal salvific will of God, and the New World was being discovered. This is when St. Robert Bellarmine first developed the distinction--or at least the terminology--between belonging to the Church "in re" (in actuality) and belonging "in voto." (by desire). St. Peter Canisius and Cardinal Cajetan also made great strides in this era. Most importantly, it was in this era that the possibility of receiving saving grave without receiving actual baptism was solemnly defined, both by the Council of Trent itself and by St. Pius V in Ex Omnibus Afflictionibus, his solemn condemnations of the errors of Baius.
But these things were affirmed before Trent as well by Fathers such St. Justin Martyr, St. Augustine, St. Ambrose, St. Basil, etc., etc. It was taught in the medieval era by Popes Innocent II and Innocent III, St. Bernard, St. Bonaventure, St. Catherine of Siena, St. Bridget, St. Albert, St. Thomas Aquinas, etc.
The three main definitions of the dogma at issue, from the Fourth Lateran Council, the Council of Florence, and Boniface VIII's Bull Unam Sanctam have always been understood this way by the Church. We can't interpret dogmas differently than they have always been--to do so is Modernism.
As an aside, just to show those definitions are still valid, here is what Pope John Paul II said in an allocution:
"Since Christ brings about salvation through his Mystical Body, which is the Church, the way of salvation is connected essentially with the Church. The axiom extra ecclesiam nulla salus"--"outside the Church there is no salvation"--stated by St. Cyprian (Epist. 73, 21; PL 1123 AB), belongs to the Christian tradition. It was included in the Fourth Lateran Council (DS 802), in the Bull Unam Sanctam of Boniface VIII (DS 870) and the Council of Florence (Decretum pro Jacobitis, DS 1351)."
All Salvation Comes through Christ
The error is limiting ourselves to only these definitions, as Bl. Pius IX explained:
"For, even if it were a matter concerning that subjection which is to be manifested by an act o f divine faith, nevertheless, it would not have to be limited to those matters which have been defined by express decrees of the ecumenical Councils, or of the Roman Pontiffs and of this See, but would have to be extended also to those matters which are handed down as divinely revealed by the ordinary teaching power of the whole Church spread throughout the world, and therefore, by universal and common consent are held by Catholic theologians to belong to faith." (Tuas libenter, Dz 1683).
Vatican II affirmed the same thing. When speaking of the possibility of salvation for non-Catholics it cites the following letter from the Holy Office (now CDF) under Pius XII which I think explains this matter well:
APPENDIX E: The First “Ottaviani Intervention”