When a psychic's prediction comes true, does that fulfilled prediction come from God?

No. The Bible is very clear warning us that even Satan can appear as an angel of light (2 Corinthians 11:14). Psychics are not getting their information from the Lord. But they might tell you they are or think they are.

They are actually tapping into the satanic realm where they are given just enough information that is somewhat true -- in order to confuse people and make them think that because the psychic was able to make an accurate prediction that it is okay to be involved such practices. But do not be fooled. Scripture forbids us to have such involvements.

"Give no regard to mediums and familiar spirits [demons]; do not seek after them, to be defiled by them: I am the LORD your God" (Leviticus 19:31).

"There shall not be found among you anyone who makes his son or his daughter pass through the fire, one who uses divination, one who practices witchcraft, or one who interprets omens, or a sorcerer, or one who casts a spell, or a medium, or a spiritist, or one who calls up the dead. For whoever does these things is detestable to the LORD; and because of these detestable things the LORD your God will drive them out before you" (Deuteronomy 18:10-12).