How do U.S. treasury yields impact yields of other sovereign debt markets?
For free-floating sovereign borrowers (e.g., Japan, Canada, UK, and the euro as a bloc (the member countries are pegged versus each other), short-term bond yields are largely determined by the expected path of the policy rate (plus a small term premium).
For longer-term bonds, one can debate how value is determined, but forward rates are generally smooth, so they can be interpreted as rate expectations and a term premium as well.
This means that bond yields ca diverge: e.g. look at Japanese bonds versus other sovereigns from 1995-2008 (at which point other countries converged at levels near Japan’s).
However, we see correlations between markets, which is not unexpected.

Central bankers might set domestic rates as a spread versus another currency, like the USD.
The business cycle is global, and new information about the outlook is thus correlated across markets.

This explains why short-term movements often are in the same direction, yet there are no reliable “rules” (since that would imply guaranteed trading profits).