What do you mean "its predecessor in that tier"? The all-but-stated goal of the 5C was to break into a new market that they'd previously been priced out of.
For weeks (if not months) leading up to the release of the iPhone 5C there were news reports of Apple's attempt to break into China by releasing a cheaper iPhone. Sure, these were based on "rumors", but since Apple almost never announces their strategy directly, this is how most of our understanding of Apple's strategy has always worked.
Apple's been able to take some market share from ZTE, but not from any of the other main players (Samsung's market share has increased since the release of the 5C).
(Also, your quotation doesn't actually refute the statement I made earlier. I didn't say that the 5C didn't sell to new iPhone users - I meant that, for those new users, the 5C sold to people who otherwise would have bought a 5S (thus eating into their potential profits). That's neither here nor there, though, since the main issue is how the 5C sold in China, not the US.)