I also had this problem, my washer is a Maytag Bravos MVWB850YW0.
When water flows into any of the cups, detergent, bleach, or softener cups it will either splash up onto the glass lid or overflow. I throttled back the water supply valves (hot and cold) to the point that the water just stayed within the cups.
I did this all within the diagnostic service mode, manual operation section, of the washer and set the water temp selection to "hot" to adjusted the hot water supply valve to keep the water within the cups. Then I set the temp to "cold" setting to adjust the cold water supply valve. I then set the water temp selection to "warm" to turn on both the hot and cold at same time to further fine tune the water supply valves.
I did this procedure for all three cups. I ran a "no clothes load" to verify that the washer will fill correctly, and within any software controlled time limits, and then continue to finish the wash cycle. All worked fine.
When water over flows the cups, the water gets under the cup lip and will rust out the washer top both from above and below.
Hope this helps.