I am not a pilot so I don't know anything about hand starting propeller aircraft. But I wonder how easily can the propeller fire up unexpectedly during the procedure even if it's done right. Whenever I see an old WWII movie and the guys are turning those big props on the bombers, I always think of that question.
When you shut down a radial the unscavenged oil in the case (oil coating the surfaces that didn't get pumped back to the reservoir tank) runs down and seeps past the rings of the cylinders directly below and to each side at the bottom. In theory, it can create an hydraulic lock if there is enough oil collected in a cylinder, that happens to be on its compression stroke (both valves closed), and the oil volume is more than the cylinder volume at top dead centre. Although an actual hydraulic lock is fairly rare (it takes quite a lot of oil), you still have to check for it because if a jug fires on start while one of the bottom cylinders is locked, it'll bend that jug's connecting rod and/or crack the head.
The engine has to be turned with no ignition/fuel to test for this. Typically it's done by hand as shown in those films. If you feel a hydraulic lock coming on as you pull through, you turn the engine the other way to back it off and can remove the lower plugs to let the oil drain out.
An aircraft could have propellers that are out of reach of the ground, or there may be some other reason, so you also have the option of doing it with the starter with fuel and ignition turned off. If there is an hydraulic lock in a cylinder the starter won't be able to do any damage on its own (it'll either bog down or its clutch will slip), so it's safe to do, if done properly.
There is always some oil collected and when the engine is cranked it goes out the exhaust valve when it opens and coats the inside of the exhaust ducting. The coating of oil takes quite a while to burn off the inside of the exhaust manifold, which is why they belch smoke for 30 seconds to minute after they start.
It IS possible to "hand start" a big radial in a fix, using things like tires slipped over the prop and pulled by a car with a rope, but not by hand unless it's a smaller radial, say under 1000 cubic inches.
The procedure you seem to refer to isn't hand starting. It's done on radial engines, with ignition off and valves locked open, to clear oil that may have settled in the lower cylinders (by seeping past the piston rings while the engine was standing) and prevent a hydraulic lock that could bend a piston rod or otherwise break things (at the absolute minimum, foul spark plugs) in the engine if cranked under power without this precaution.
Unless there's something very deeply wrong, the engine can't start with the ignition off. Engines of the size you'll have seen this done for, however, are never hand started. Either ground starting carts were used to supply battery power for electric starters, or cartridge starters were used to get the engine spinning so the magnetos could fire the spark plugs.
Hand-propping was only done on small engines, not bombers or even fighters. It can still be done on small engines today. One of two conditions must be met. Either the ignition must be on. Or, the magnetos are not properly grounded.
Turning a prop past its compression point could cause the engine to fire through as many cycles as the available fuel will allow. Even a few degrees of turning through the arc could cause this to happen.
One of the two magnetos will normally have an impulse coupling on it to assist in spark generation during very low RPMs. Slowly cycling an accidentally ungrounded magneto can cause a horrific accident. This is why you should shut down the engine by starving the engine of fuel. That way, no fuel is left in the cylinders in case of accidental spark.
Also, make sure the mag switch and master switch are off before approaching the front of the aircraft. Lastly, perform a p-lead check just before shut-down.
An automotive example of this danger can be found on old diesel trucks with mechanical, engine-driven fuel pumps. If the fuel shutoff was not engaged, the truck could start itself if it were allowed roll a few feet. Even with no one at the controls.