Rising water in the other bowl points to an interaction within the connected drainage. It does not establish that the disposer motor needs replacement, especially if the motor was not running at the time.
What the observation tells you
A shared or linked waste arrangement can let one discharge affect the other bowl. Stop adding water before either bowl overflows, and keep food out of the disposer. Do not block one bowl and force water through the other as an improvised test.
A useful next step
Photograph the accessible pipe layout and describe which bowl was emptied. Ask for the sink drainage arrangement to be assessed before authorising work on the grinding appliance alone.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.