The eyewitness also states that Nero rushed back to organise help for his people by opening his own gardens as a shelter for the homeless. Regardless of that Nero was not a popular emperor and as the same eyewitness state
"for a rumor had spread that, while the city was burning, Nero had gone on his private stage and, comparing modern calamities with ancient, had sung of the destruction of Troy"
The adage he played the fiddle while his city burned reflected this, it was propaganda.
Also, what we know as the fiddle was not around at the time.