Sidebands in spin-oscillator coupled devices

I am researching spin-oscillator hybrid devices (particularly those coupled to NV centers), and I have come across this paper investigating the strain field of a cantilever and its effect on the NV centre.

I don’t fully understand the sideband concept in this context. I know it’s used for radio modulation but I cannot fully grasp why it is important in spin-oscillator coupled devices. Also Fig. 3 does not make sense to me. So when no strain field is applied, we observe the hyperfine structure of NV (0, 1 and -1), but when we move the cantilever at its resonant frequency sidebands arise? Why?

What is actually the carrier signal mentioned in Fig 3? From the equivalence of figures, wouldn’t it be the frequencies of normal NV transitions? If that is the case, why does the carrier signal disappear when the sidebands can be resolved the most (when the cantilever is at its resonant frequency)?

Thank you in advance!