The staggered flow is normal _during bleeding only_ .

A single circuit master cylinder ( or clutch master cylinder ) has a piston directly actuated by the push rod.

A dual circuit master cylinder ( tandem master cylinder used since the 60's ) has a floating secondary piston ahead of the actuated primary piston. When the system is full of fluid, there is a column of fluid between the two pistons. As you push the primary piston fluid comes out of the rear port and also pushes the floating secondary piston. Fluid ahead of the floating piston then exits the front port.

If you have a leak in one circuit, that piston must bottom out until the good side can make pressure.

Dual circuit masters split the brakes front to rear on rear drive cars , diagonal on front drive cars and triangular on older Volvos where 1/2 of each front caliper and one rear are on one circuit.

Generally swapping lines on ports isn't done. In a disc / drum system the drum side circuit has a residual pressure valve ( 2 to 6 PSI ) that keeps a bit of pressure in the system, this keeps the wheel cylinder cups expanded to prevent leakage. ( Sometimes on a race car a RPV helps reduce peddle travel on a disc system. ) Brake balance will be off with a stepped bore MC if you swap.

Brake peddle ratio ( ultimate pressure ) can be influenced by master cylinder diameter. Assuming the same foot peddle pressure. A small bore will make higher pressure but need more travel to make the same volume. A large bore will have lower pressure, higher volume and need less travel.

Some master cylinders have a stepped primary / secondary bore ( 2 diameters ) This can be used to design in front to rear brake balance.

Other times the primary piston is further split into two bore diameters, the large diameter provides large volume to push the front caliper pistons to the rotors. As pressure rises, fluid is bypassed from this area and the smaller area provides needed pressure ( leverage ).

Have a look at general fluid power ( hydraulic / pneumatic ) theory for how a hydraulic system works.

If you install calipers with larger pistons and don't upsize the MC bore, you will have long peddle travel.