The arrangement depends on the sink and waste kit. An overflow may connect into associated waste pipework, so dampness near the disposer can originate from a separate route around the bowl.
What the observation tells you
Do not deliberately overfill the sink to test it. A photograph showing the accessible overflow hose and where it joins can help an engineer distinguish connections without guessing from a close-up of one wet patch. Avoid pulling tubing to improve the view.
A useful next step
Report whether water reached the overflow before the leak was noticed. Treat the overflow and disposer as parts of the sink's water path while keeping their individual components clearly identified.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.