He sounds surprised, unsure of how to present Jewish accusations to the emperor, now that Paul has appealed to Caesar. Actually, Festus is doing his usual politicking. But one thing he acknowledges and gets right:
Instead, they had several arguments with him about their own religion and about a certain Jesus who had died but whom Paul kept claiming was alive.
Acts 25.19 NET
Though the previous narrative doesn't mention it, since Luke probably takes it for granted by now, after so many examples, is that Paul always preaches the living Jesus. He may be put before governors and kings for his own defense, but he doesn't let an opportunity go by without getting in a word about the gospel.
Note the imperfect verb referring to Paul: He "kept claiming" Jesus was alive. Paul was insistent. He never let up on this point. He only knew one tune to sing.
When people turn the attention to you or try to get you off track, what do you do?
The Christian never forgets that the subject is always Jesus Christ who died to save men, who lives again, and who will judge the world.
Others have their agendas and objectives. Keep yours as well, the gospel of Christ.
God who puts men in their place, put the words of Christ in my mouth, regardless of where I am.
Hold this thought: Keep speaking about Christ, everywhere.