The scriptures teach that a major event happened when Christ died--which was just after his declaration that "It is finished" (that was his last breath). So roughly simultaneous to this declaration, was what occurred in the temple in that moment.
45 And the sun was darkened, and the veil of the temple was
rent in the midst. 46 And when Jesus had cried with a loud
voice, he said, Father, into thy hands I commend my spirit: and having
said thus, he gave up the ghost. (Luke 23:45-46, KJV)
Other versions of the story give similar evidence, along with additional detail.
37 And Jesus cried with a loud voice, and gave up the
ghost. 38 And the veil of the temple was rent in twain from
the top to the bottom. (Mark 15:37-38, KJV)
50 Jesus, when he had cried again with a loud voice,
yielded up the ghost. 51 And, behold, the veil of the
temple was rent in twain from the top to the bottom; and the earth did
quake, and the rocks rent; 52 And the graves were opened;
and many bodies of the saints which slept arose, 53 And
came out of the graves after his resurrection, and went into the holy
city, and appeared unto many. (Matthew 27:50-53, KJV)
So the priest who was officiating in the temple at that hour might have been horrified to see the veil between the holy place and the most holy place torn apart, such that he, and all others peering through the opening, could look into the most holy place--the place that traditionally the high priest had entered only once a year, on the day of atonement, with great soul-searching and reverence lest he be struck down by a holy God for having profaned His sanctuary. No common citizen, or even most of the priests, had ever before been permitted to look into the most holy place, and now, not only can the priest see inside, but anyone can.
The most holy place did not at this time house the ark of the covenant. To preserve it in a time of peril, centuries earlier, the priests had hidden it away in a secluded location--where it presumably remains to this day, not yet having been discovered (though many have tried to claim they've found it). So the Shekinah glory had long since been absent from the sanctuary, and there was no danger of a recurrence of the slaughter of Bethshemesh (see 1 Samuel 6:19).
Still, the ritual of entering the most holy place but once a year, and only by the high priest, had been preserved until the time of Jesus' death. And when the priest witnessed the veil being torn, from top to bottom--obviously not by human hands, he would have been astonished. The shock would have been too much for words. In place of saying "it is finished," the priest would have stood dumbfounded, unable to continue his normal service. The lamb he is about to slay, escapes from his hand, and he has no strength, nor mind, to prevent it.
There is no record of the priest saying anything at this moment. The horrific desecration of the sanctuary by the supernatural rending of the veil would have caused all who stood by to tremble--as also the earth did, the earthquake being recorded in Matthew's account of these scenes. In times of such astonishment and shock, people's voices fall silent.
There is no record of the officiating priest uttering anything at the time of Jesus' death; nor should such an utterance be expected. The major event which occurred at the temple, witnessed by all present, was the rending of the veil, permitting all to see into the most holy place. This was accompanied by an earthquake. No words are on record as being spoken by anyone there present at the temple at that moment.