If one is careful to load the chain straight and get the press pin exactly lined up with the tool pin it doesn't matter if the plates are flat or flared as far as I've found. Once the tool begins to work on the chain's pin it is being held in there with enough force that the chain will not move or twist as long as it is not torqued relative to the tool during the break/press operation. The tool is exerting hundreds if not thousands of PSI when it is doing its job. Like I said before it is quite capable of producing enough force to self-destruct if the chain isn't situated in such a way that the pin will give first before the tool eats itself. Always be aware of that and pins will break much less often.

Don't let it twist or bind and carefully watch what is going on within the tool with regards to the chain orientation. If in doubt while using the tool let up on it and reposition. I've never had a chain that I had too much trouble with. Perhaps I've just yet to come across a chain with enough of a flare on the sideplates to make this impossible. Then again I am used to working on motorcycle chains which are much bigger and orders of magnitude tougher than a bicycle chain while the chain-breakers available seem to be actually weaker and more fragile than bicycle breakers.

It is REALLY easy to break a press pin on a $100 chain press on a 620 motorcycle chain. In fact, I avoid using a breaker on a cycle chain and only take a chain off when I want to BREAK it and replace with a new one when it is worn out. I use the motorcycle chain press only to "rivet" or peen the special master link of a motorcycle and don't abuse it trying to break a chain. That is what side-grinders are for.

Bicycle chains with a good tool like the CT-3 are cake in comparison.