When the question asks what 'harmonic device' is being used, what does it mean?

You could think of a 'harmonic device' as a 'harmonic technique' e.g. circle of fifths or chromaticism. When a question is asking what harmonic device is being used it is likely to be very obvious e.g a chain of suspensions rather than a single one or a complete circle of fifths rather than just a few steps.