So, for 200 years, EM bonds have been hit when DM yields rise. It's not new.
What is new then? As EM to EM business has surged, and EM savings have boomed, so the ownership structure has changed.
Now EM investors constitute the core of EM bondholders. So, the sell off makes less sense, it is being driven by the marginal holders.
In short, there is already value in EM bonds.