I have 3 good task widgets on my Home Screen, each being a different list.
For whatever reason, one of them often goes back to "today" rather than the specific list I set it for ... oddly, it's the same one each time. I have deleted and re added and getting the same behavior.
I'm not quite sure what the exact situation is. First, try restarting the device. If this doesn't help, re-add the widget that have the issue. Last one would be running 'Settings - Advanced - Reset calendar connection'. This will make you to reset all list related preferences such as smart lists and quick actions though.