That’s the final judgment, not the judgment of the believers, who are his Bride and already with Him in heaven.
Even at the particular judgment — at the moment of our deaths, Christ can send us either to heaven or to hell or to Purgatory.
That is not what the Catholic Church teaches. It is what you profess. Of course it would be different.
The particular judgment will be instantaneous, and some say that in the moment of death the soul is illuminated as to its own guilt or innocence and of its own initiation takes its course either to hell, or to purgatory, or to heaven. St. Paul said: "Who show the work of the law written in their hearts, their conscience bearing witness to them, and their thoughts between themselves accusing, or also defending one another, in the day when God shall judge the secrets of men by Jesus Christ (Romans 2:15-16).
So there we have, it seems to me, the Particular Judgment, with God judging the secrets of men by Jesus Christ.