When did the Catholic Church stop teaching that salvation is only available through them?
When did they start? It was when Jesus asked them to spread the Good News of Salvation as far as they could. The Church/catholic Assembly taught the way of salvation as they had learned it from Christ, the Word of God, the Son of God. They had no authority to teach it any other way.
Fifteen hundred years later, division occurred. The Church continued to teach the only way of salvation they had been given authority to teach. No matter how many ways to salvation are taught today, the Church stands firm in teaching what from the beginning they were told by Christ and the Apostles to teach.
If Buddhists, Hindus, Taoists, Muslims, Jews have authority to teach another way, so be it. Catholic Church teaches only the way to salvation that Christ gave her the authority to teach: Repentance for the forgiveness of sins; that he is the Son of God; his way is truth and life; follow his way and his teachings into salvation. Note, that one of Jesus' final prayers was that his followers remain one.
Interesting and ironic, is it not: Other Christian denominations broke away, ignoring Jesus' prayer, but have the confidence they can still teach all that Christ taught. But then, since the first sin, we have been a broken people and God still manages to work with us. Yet another break on his people's part does not weaken God in any way. His determination to draw people to himself never wanes and is never thwarted. The Catholic faith recognizes this--that broken as God's people are, we all still remain in the hands of a merciful and loving God. And always have been.