Realistically, Europe has been as big of a friend to US bond markets as the Fed.  If it weren't for Greek concerns and the mounting systemic crisis, US bond market pain in 2010/11 would have been much worse.  That crisis gave US bond market participants a reason to step in and buy again.  And the broader European economic malaise that followed prevented the US from doing what it might have otherwise done. 

But 2014 is when things really got serious.  It's not marked on the chart above, but you may recall that mid-2013 was all about the taper tantrum, and it's the reason US yields diverged so sharply from EU yields.  The Fed was signalling a pull-back and things looked grim by the end of the year.  Then in early 2014, the ECB announced it was working on true QE--something previously thought to be impossible within the EU's legal framework.  

As the ECB wrote its own version of "The Little Engine That Could (do QE)," US bond markets began to calm down.  Brexit followed closely and suddenly, US 10yr yields were back to all-time lows.  

Post-Trump election, and EU bonds faded to the background while the US bond market was tending to its own concerns (economic strength and Treasury issuance skyrocketing).  It wasn't until the "global growth concerns" ramped up in late 2018 and the trade war in 2019 that we began to consider (or "remember," perhaps?) global economic interdependencies and thus the implications of movement in the world's other major bond markets.

Then, there's covid.  Notice how very small the reaction has been in Europe.  It's as if European yields were already positioned for some harsh new economic reality and US yields simply closed the gap (with help from the Fed, of course).  After closing said gap, there's been "just a bit" of renewed correlation:

Is it time once again to look to shorter-term volatility in European markets as a guidance-giver for US bonds?  Maybe.  There will be instances like the past 24 hours where EU bonds seem to be sending a stronger message than US bonds, and when that happens, we'll be making a note of it.  That argument can probably be made so far this week.

Whether this is an ongoing phenomenon or simply a byproduct of both yields being extremely low and sideways in the bigger picture remains to be seen.