It sure smells like this passage means to say the terrible things that happened to Jesus were predestined. If a person wants to quote this passage to show that The Passion was predestined, there are several problems with the argument.
(1) It is risky exegesis to draw critical doctrine out of something the Bible quotes someone as saying if the person is not speaking by divine inspiration. The exegetical method is more common than we might think. Consider John 9:31. A man was born blind and Jesus healed his sight. Jesus did not introduce himself; but the man was able to conclude that Jesus was a righteous man. He said that God does not listen to sinners. It is terrible exegesis to conclude that God does not hear the prayers of sinners based upon what this man said. He was not speaking from divine inspiration (Acts 10:31. See also 1 Kings 8:41-45). On a similar note, Peter’s personal judgment in Acts 1:21-22 is frequently quoted as proof of the qualifications of an apostle. Peter was not speaking from divine inspiration. He decided on his own to set a precedent that there should be twelve apostles. He offered his short list of qualifications was a suggested rubric for selecting replacement apostles. Bad exegesis, although Paul seems to agree with qualification #2, that an apostle must have seen the risen Lord (1 Corinthians 9:1).
(2) It is not clear how this passage should be punctuated. Greek scholar Adam Clark believes verse 28 should be read as parenthetical (see below).
Clark suggests that verse 28 ought to be read parenthetically; but watch what happens when we remove the verse numbers and two commas.
For in this city, in fact, both Herod and Pontius Pilate, with the Gentiles and the peoples of Israel, gathered together against your holy servant Jesus whom you anointed to do whatever your hand and your plan had predestined to take place.*