I am dual US-South African and I've always checked in with the passport I intend on entering the next country with. I routinely check in with my ZAF passport on ATL-JNB, and of course check in with my USA passport on JNB-ATL, and I've never had any issues with CBP.
Then at passport control in JNB on the outbound, I present my ZAF passport (despite "flying" on the USA passport).