Leviton 3-way smart switch works, but I think it's wired incorrectly!

[nickelcanuck]

I installed a Leviton smart switch in a 3-way circuit and the corresponding coordinating switch in the picture (right switch). The lights function as they should using both switches.
However, I recently was about to install another switch on left side of the box, when I looked at the coordinating switch and discovered that I probably wired it incorrectly. I believe I erroneously connected the neutral terminal on the coordinating switch to the neutral of the other circuit.
The circuit on the right only has one bundle of wires coming in with 3 wires: red, black and white. I believe the red is a traveler, black is the line/traveler and white is the neutral? The instructions for the switch had me capping off the black wire.
In this case, would I need to connect the neutral of the coordinating switch to this yellow wire cap with the the black and white?

 

[BenCos18]

In this case, would I need to connect the neutral of the coordinating switch to this yellow wire cap with the the black and white?

neutrals are likely common as they are on the same circuit
just tie the neutral for the swcond switch in with the neutrals for the other switch