Not that I make a point of breaking taps, but it seems like they can never deliver enough torque to break the chip. They're the Cone of Silence of my shop, great idea, never work like they're supposed to.
Sometimes I read more into what others say than I should. This might be one of those times. I would never try to advance the tap to break the chip. I only break off the backward chip that has already been started when the tap broke. In that sense, nothing new is being cut, just whatever has started to lift from the trailing edge.
I've never tried to examine what happens, but I'd expect that turning the tap backward only clears an already started chip.
In any event, I never try to do that in one motion. I wiggle it backward and forward a smidge at a time. I don't force anything. In that way, the tap breaks the chip much like wiggling a piece of burr would break when you wiggle it back and forth. Sometimes it takes a lot of wiggling, but it's VERY satisfying when it finally turns back a full flute with virtually no effort.
Perhaps it helps to visualize the process the way I do - it's like bending the started chip back and forth till it fails in fatigue.
I will be honest, I have no idea where I got those instructions or even if I ever did get them from a source. They might well be the product of my own sick mind.
What I can say for sure is that my garbage taps have given me lots of practice in recent years. I don't recall having early problems though. That would be back in the days of holding a drill bit and a tap up against a window to see how much the tap is cutting..... Back then, I prolly had much bigger holes than I use today!
Ive now had a chance to check my tap sets. My oldest two sets (small metric and small imperial) are both HSS. My two big sets are both "Alloy Steel" but one is titanium coated and the other is tungsten coated. They are both that gold colour. I fully expect that the tungsten coating is an error and they are really titanium coated too. They are made in China.