Thanks for the response. It really doesn't bear directly on my situation, but it does have references to what I need in RFC 8365.
Now that I know the terminology for these features, "Split Horizon" and "Local Bias" (neither of which seems to fit very well to me), it's easier to find more info.
I understand the approach outlined in RFC 8365. Makes it look more like something is not working right in our implementation. I did some definitive packet captures showing that BUM traffic is going in the non-designated member of the ESI and looping back out of the designated forwarder. Not all BUM traffic is looped, just a small fraction. I want to investigate next if the events have something to do with MAC address tables or some other timers.
The switches doing it are two Arista 7050SX3 with a single instance VXLAN EVPN. It should be a pretty simple setup. Not aware of any knobs to modify any of this behavior or what we could be missing.