This is a question regarding a rather fine point of doctrine - exactly when does the bread/wine become the Body/Blood of Our Lord Jesus Christ?
Orthodox theologians (which includes, AFAIK, Eastern Rite Catholics) believe this happens at a point in the Mass called the Epiclesis. Latin theologians believe it happens at a point in the Mass called the Anamnesis. Both Eastern and Western liturgies incorporate both, so the distinction is irrelevant to the person in the pew.
In the Latin Rite, the Epiclesis immediately preceeds the Anamnesis (and bells are rung at the Epiclesis when bells are used). The Epiclesis is the part where the priest invokes the Holy Spirit, such as: “Let your Spirit come upon these gifts to make them holy, so that they may become for us the body and blood of our Lord, Jesus Christ.”
In the Latin Rite, the next sentence is the Anamnesis, which is the Greek word used the Bible for “remembrance” and recounts the enactment of the Last Supper (“On the night he was betrayed…”)
In Orthodox liturgy, the order is reversed. It begins with the Anamnesis, and concludes with the Epiclesis. But both liturgies incorporate both elements.
As far as I know, the Church has never definitively taught either viewpoint as a matter of doctrine. Any Catholic may hold either opinion. Personally I favor the Eastern position because it seems “cleaner.” The Latin position leaves me wondering - does the consecration happen at the words, “this is my Body” or “this is my Blood?” If the priest got shot after saying, “This is my Body,” would it still be Eucharist? Would the failure to consecrate the wine invalidate the Sacrament? I have no idea (the doctrine of concomotance suggests that everything is OK, but it still seems messy). The question seems messy to me, and I like things to be nice and tidy. The Eastern viewpoint offers tidiness.
But, either way, all the bases are covered.