False!
John 19:28, ". . . Jesus knowing that all things were now it is finished [τετελεσται], . . ."
I understand that you believe it to be false.
Using your method the only way that Jesus could have said "it is finished" and indicated the totality of his mission would for him to die and then all of a sudden gasp "it is finished" as a mini-resurrection.
Jesus had accomplished all that He had come to accomplish in terms of becoming "flesh", taking on our infirmity. What was left was Him to commit His Spirit to the Father and die. His work was done. His "mission" of redemption was accomplished. He had submitted to suffer and die under the powers of this world (the powers of sin and death) at the "hands of wicked men".
John 19:28-30 After this, Jesus, knowing that all things had already been accomplished, to fulfill the Scripture, *said, "I am thirsty." A jar full of sour wine was standing there; so they put a sponge full of the sour wine upon
a branch of hyssop and brought it up to His mouth. Therefore when Jesus had received the sour wine, He said, "It is finished!" And He bowed His head and gave up His spirit.
His earthly mission was done. It was accomplished. And He committed to the Father His Spirit.
Have you ever considered that the reason you believe that there were "two deaths", and the reason PSA advocates strongly look to a "spiritual death" not actually mentioned in Scripture as being redemptive, may be that you are too focused on Jesus' death apart from Jesus' life? His death (as with our deaths) are the culmination of a life lived on this earth. His "blood shed" is His life given which begins when He humbled Himself and became flesh. The "atonement" (which more accurately is His "reconciliation") encompasses much more than dying on the cross.