Psalm 78:2 speaks of teaching through parables and declaring matters hidden from ancient times. The psalmist uses this method to communicate wisdom drawn from Israel's sacred history. The verse itself does not specifically predict the tone or authority with which the Messiah would teach.
Matthew 7:29 says that Jesus taught with authority unlike the scribes, while Matthew 13:35 directly applies Psalm 78:2 to His use of parables. The stronger fulfillment therefore concerns the form and revelatory purpose of Jesus' parabolic teaching rather than Psalm 78 predicting His authority as such. His unique authority is established throughout the Gospels, and His parables reveal divine wisdom in a way that brings the psalm's pattern to a distinctive fulfillment.