I had one die because I had the filament voltage set wrong.
The 35C5 may have developed a heater cathode short which caused the hum. Since the radio uses the 35C5 it must be a series set. The rate at which it warmed up would be different in the tester which has a transformer.
Since they have you set the filament switch to F for this tube it would only apply 25V to the filament. This shouldn't have been very stressful. Of course if you set it to G...
John