Each photo that is part of a 360 scene should be shot with the same exposure settings. All one-shot 360 cameras will handle this for you, matching your exposure choices across their multiple lenses and sensors. But DSLRs and mirrorless cameras should have all exposure controls set to manual and locked to the same settings for each shot that goes into a composite 360 photo.
This is a fundamental requirement for best practise professional 360 photo work, and the reason is simple: a 360 photo is created from at least two and normally more shots that are patched together to appear as one continuous image. If the exposure is different from one shot to the next, this is likely to look like uneven lighting at best and at times a distracting patchwork of exposure areas.
Having said this, it’s not impossible to shoot using auto exposure settings. If there’s a lot of overlap between shots then the stitching software can blend lightness levels across the scene, and the results can look good. This allows someone to expose for a bright window and then differently for a dark corner. However, this comes at the expense of accurate, consistent tones across the shots – for example where a flat, evenly lit wall runs through both photos – and as a result it is not considered best professional practise.
Assess the brightness and shadow areas of the complete scene. You may wish to settle on an exposure that’s simply averaged between the extremes, or you may prefer to expose for the most important parts of the scene and deal with any bright and dark areas in post-production or simply let them peak or fill in.