I would call that a reverse (of commonly misunderstood) cause and effect, rather than common cause.

Bond yields and bond prices are not linked by cause and effect, because they are closer than linked. They are just two measures of the same thing.

So that thing (lower bond prices) may cause money to flow into bonds, as opposed to the OP idea that money flowing into bonds should cause higher bond prices.

I intentionally mentioned that opposite (in both direction and correlation) cause and effect as one possibility. But my main point remains that the two things are more likely just independent. Prices can go up and down in markets without being caused by or causing a flow of cash in or out.