defaultdict not synchronized in python3's multiprocessing

Question

I'm having this problem for a little while and haven't figured it out yet, i.e., how to synchronize a dictionary across children processes. This is typically useful when trying to process a bunch of files independently while keep track of some stats regarding the files/datasets.

With useful tips from: Using defaultdict with multiprocessing?, i came up with something similar to this:

class MyManager(BaseManager):
    pass

MyManager.register('defaultdict', defaultdict, DictProxy)

def partial_test(string, multi_dict, idx):
    k = string[idx]
    multi_dict[k].append(idx)     // record indices, failed!
    // multi_dict[k] += 1         // this works as expected!

def job():
    mgr = MyManager()
    mgr.start()
    multi_d = mgr.defaultdict(list)

    pool = multiprocessing.Pool(processes=4)
    partial_job = partial(partial_test, 'mississippi', multi_d)
    N = len('mississippi')
    pool.map(partial_job, range(N))

    pool.close()
    pool.join()
    print(multi_d.items())

The output is:

[('m', []), ('i', []), ('s', []), ('p', [])]

For my application, I had to use partial() with pool.map(), but then the dictionary didn't get updated properly. Also, as i mentioned above, if multi_dict was used as a counter as in the link's example, everything worked as expected (definition changed to defaultdict(int) of course). Anybody knows why?