Hi Smaultre, when measuring light with an optical power meter, you always measure the "broadband" power. The only thing the wavelength setting does is adjust the correction factor of the photo diode to convert to power for that specific wavelength, but it is not possible to measure the power of a specific wavelength from a broadband source.
When I connect the HP 70951 light source to a VIS-power meter, I get -20.4dBm, when I connect it to a NIR power meter, I get -8.2dBm (both set to a wavelength of 850nm). This means it also makes it hard to compare results, as the sensitivity spectrum of the photo diode is different for different power meters. As you measure around -9dBm, I expect you are also using a NIR power meter (InGaAs sensor or Ge), but this does certainly not mean your source has a slightly lower output.