Many telecom operators have a special code that is used for recording. When you're making a call, you or the other party may press the record button. This will save both the input via microphone and the output via the speakers as one audio file for future use. When you press this button a special code is sent back to the telecom.
Until recently most places in the USA did not do anything with this code. But now it's catching up to the rest of the world. Once this is pressed, a voice will tell both parties that they are being recorded in the recording. This is so that you can't later say "I didn't know they were recording me!" and if you have every-party consent laws, then that recording is illegal so it cannot be used as evidence and the person recording could actually be charged with a crime.
You can start the recording with an accidental face press, pocket press, keypad entry, or a malicious app. If either of you accidentally started it, then there's your answer. If neither of you did, then most likely one of you is infected or one of you were connected to a relay tower decrypting your calls and then passing them through to a real tower. Whoever was operating this relay station was a n00b idiot though. Both are concerning.