Using OBR, Legion and/or Fed, I was in B with a runner on first with one out and the plate umpire gave me the double index finger point to first base, then to third base indicating that he'd cover 3B on an out/safe call in the event there was a single to say RF, which I stayed and covered 1B and 2B. I mimicked his hand-signals, aka, repeated his hands signals. He told me between innings that an umpire is supposed to provide hand-signals to indicate what thy own self would be doing, not regurgitating what I saw him do to confirm.
So, when you give a hand-signal like the one above as a field umpire, do you do it to confirm the plate umpires hand signal or do you give a hand(s) signal that indicate what you yourself will be doing or going?
The short answer is that inter-umpire signals are not standardized but are set by prior agreement - either within the association or as decided in the parking lot during the pregame between the umpires themselves.
When I was relatively new to umpiring, I did a game with a guy who used a very extensive set of signals. With a couple of guys on base, he almost looked like a third base coach. I just nodded back to him and hoped I was covering the right things
As Mark has indicated, signals are a convention, decided upon by local association or simply between umpires prior to the game.
In my chapter, the umpire inside is instructed to return the signals to the plate to indicate awareness of the situation.
But your partner was correct in that his signals indicate what HE is going to do and your mechanics adjust accordingly.