Should I include the tableData property to my IPerson interface?

No, because you will probably use your IPerson interface throughout your application, and adding a tableData property that may or may not exist (see below) will defeat the purpose of typechecking. Typescript is telling you that tableData doesn't exist on your IPerson interface, which is correct. However, the underlying Javascript from your dependency has appended your object with a tableData property for its own internal purposes (and external if this is the only way to get at the index) and didn't bother to let Typescript know. Your code runs, the index is available for use.

There are probably better ways to do this, but you could create an IPersonAfterRowUpdate interface that has the tableData object on it:

interface IPersonAfterRowUpdate extends IPerson {
  tableData: { id: number };
}

/* ... */

onRowUpdate: (newData, oldData) =>
            new Promise<void>((resolve, _reject) => {
              setTimeout(() => {
                if (oldData) {
                  const updatedData = [...data];
                  const index = (oldData as IPersonAfterRowUpdate).tableData.id;
                  updatedData[index] = newData;
                  setData(updatedData);
                  resolve();
                }
                _reject(new Error('Could not find oldData'));
              }, 1000);
            }),

Notice we have to check that oldData exists otherwise TS wouldn't like us indexing updatedData with a possible undefined value.

Then submit a PR to this library with this function typed correctly!