Was Satan "behind" the crucifixion of Christ?
First we must define "behind." Did Satan, humanity's advisory, play a part, by deceiving Eve and facilitating Adam's volitional sin? Yes.
Did God's predetermined plan to put Christ to death, Acts 2:38, originate before Satan tricked Eve? Yes
When was Christ known as the Lamb of God? Was it before creation or before the Fall? Yes
So Satan was "behind" the crucifixion only because God was behind Satan.
Next we need to define "instigator." The Greek word "Loimos" (G3061) is translated as "instigator" in at least on version of Acts 24:5, but usually "pest, plague, or troublemaker" are the translation choices. No doubt Satan caused "trouble" for Adam and Eve!!
Did Christ die in our place as ordained (predestined) by God? Nope. Christ died for the whole world, all of fallen humanity, to provide the means of reconciliation for all humanity. But wait, there is more, Christ has provided the actual reconciliation, salvation, for each and every individual God has put into Christ's spiritual body.
The fly in the buttermilk is the well hidden agenda of teaching "Limited Atonement" (Christ did not die for all humanity) stuffed into the fabric of PSA.
Christ's substitutionary sacrifice provided our means of reconciliation (Salvation) and provided our reconciliation (Salvation) when God transferred us out of the realm of darkness into the kingdom of His Son.