Is it necessary?
Is it necessary from a technical perspective? I'd say "no", but we usually do. the injector delivers a volume, and your sample and standards are a certain concentration (such as nanograms per microliter) so an injection of (for example) 5 µl would still deliver the same number of molecules of analyte no matter what the solvent is. However, if the injection volume is large, and the solvent is a "strong" organic solvent, the solvent injected can affect the chromatography; so in that case the response would be "yes", and to match solvent type.
In the regulated world, follow whatever was validated and documented by your company. We use (at least) one validated assay where the calibration standard is made up in Organic Solvent 1, and the samples are extracted with Organic Solvent 2. The mobile phase is an aqueous-organic mixture containing neither Organic Solvent 1 or Organic Solvent 2. For this our injection volume is 5 µl.