I see a lot of people making comments that imply a basic misconception around how manual priority works.
Manual priority mode does not supersede the basic task priorities. It modifies them. With Manual Priorities unchecked, every colonist prioritizes tasks on the left over ones on the right. With the option checked, you create tiers of priority, with each priority tier respecting that basic left-to-right hierarchy.
Example:
Lorenzo is my researcher/cook/warden. By the normal mode, he will almost never research (since researching is to the right of everything, even hauling and cleaning). It's early game, so I need everybody to be willing to do everything, but I'd still like him to start researching more often. I set his priorities to:
Firefighting 3 Doctoring 4 Warden 3 Cooking 3 Hunting 4
Constructing 4 Repairing 4 Growing 4 Mining 4 Plant Cutting 3
Crafting 4 Art 4 Hauling 4 Cleaning 4 Researching 3
Lorenzo's task priorities are now, in order:
(tier 3) Firefighting, Warden, Cooking, Plant Cutting, Researching
(tier 4) Doctoring, Hunting, Constructing, Repairing, Growing, Mining, Crafting, Art, Hauling, Cleaning
Lorenzo will now research whenever there are no fires, prisoner responsibilities, there are enough meals to satisfy my bills, and no trees to cut. He will occasionally engage in lesser tasks, but only rarely. In particular, he will almost never choose to do medical tasks but I can still assign him to do them if my primary doctor gets hurt, so I can manually select him to heal my doctor.
Note that Lorenzo's task selection is independent of the other colonists' choices. Also note that nothing needs to be selected as Tier 1 or Tier 2 in order for this system to work this way.
More complex example:
Firefighting 1 Doctoring 4 Warden 3 Cooking 2 Hunting 1
Constructing 4 Repairing 4 Growing 4 Mining 4 Plant Cutting 3
Crafting 4 Art 3 Hauling 2 Cleaning 1 Researching 2
In order from most likely to least likely, Lorenzo's task priorities are now:
(tier 1) Firefighting, Hunting, Cleaning, (tier 2) Cooking, Hauling, Researching, (tier 3) Warden, Plant Cutting, Art, (tier 4) Doctoring, Constructing, Repairing, Growing, Mining, Crafting
Understanding the nuances of the manual priority system really helps alleviate my micromanagement needs, while still allowing me a great deal of flexibility when I want to direct-assign tasks. I see a lot of Let's Play videos where players are constantly returning to the Work tab during emergency situations. If you set colonists to do every task they can at tier 4 while organizing their workload based on skillset and colony needs at the higher tiers, you will pretty much only need to return to the Work tab when you acquire new colonists.
I hope this helps your gameplay, and if I've misunderstood the system, please let me know.