In fact, it wasn't until the very end of the apostolic age that the Jews, seeking a new focal point for their religious practice in the wake of the destruction of the Temple, zeroed in with white hot intensity on Scripture and fixed their canon at the rabbinical gathering, known as the "Council of Javneh" (sometimes called "Jamnia"), about A.D. 90. Prior to this point in time there had never been any formal effort among the Jews to "define the canon" of Scripture. In fact, Scripture nowhere indicates that the Jews even had a conscious idea that the canon should be closed at some point.
The canon arrived at by the rabbis at Javneh was essentially the mid-sized canon of the Palestinian Pharisees, not the shorter one used by the Sadducees, who had been practically annihilated during the Jewish war with Rome. Nor was this new canon consistent with the Greek Septuagint version, which the rabbis regarded rather xenophobically as "too Gentile-tainted." Remember, these Palestinian rabbis were not in much of a mood for multiculturalism after the catastrophe they had suffered at the hands of Rome. Their people had been slaughtered by foreign invaders, the Temple defiled and destroyed, and the Jewish religion in Palestine was in shambles. So for these rabbis, the Greek Septuagint went by the board and the mid-sized Pharisaic canon was adopted. Eventually this version was adopted by the vast majority of Jews - though not all. Even today Ethiopian Jews still use the Septuagint version, not the shorter Palestinian canon settled upon by the rabbis at Javneh. In other words, the Old Testament canon recognized by Ethiopian Jews is identical to the Catholic Old Testament, including the seven deuterocanonical books (cf. Encyclopedia Judaica, vol. 6, p. 1147).
But remember that by the time the Jewish council of Javneh rolled around, the Catholic Church had been in existence and using the Septuagint Scriptures in its teaching, preaching, and worship for nearly 60 years, just as the Apostles themselves had done. So the Church hardly felt the obligation to conform to the wishes of the rabbis in excluding the deuterocanonical books any more than they felt obliged to follow the rabbis in rejecting the New Testament writings. The fact is that after the birth of the Church on the day of Pentecost, the rabbis no longer had authority from God to settle such issues. That authority, including the authority to define the canon of Scripture, had been given to Christ's Church.