Do tube amp record players need to warm up before playing a record?

Zenith Cobra-matic Model HF10 Chassis 3Z04

I let the tubes warm up for a few minutes and played the record. It played fine and the audio quality was decent and then I heard some popping sounds coming from the amp. 2 of the 3 tubes are lit up and the third one (12AX7) isn't. Did I damage the tube?

You didn't damage the tube; it just failed by its self.