That should be the correct set of contacts.
Aux contacts will get a build-up "crud" on the contact surfaces when contaminants in the surrounding air get into the contact chamber. Load switching and arcing will usually burn that off, but without that arcing it just gets worse and worse. Then when the resistance increases, it becomes like a heater and heats up, EVENTUALLY burning enough off to allow better conduction. That burn-through process looks like a time delay. In this case because you are only switching a small relay, the load on those contacts is probably so light that this is happening.
Some manufacturers built in a "wiping action" in the way the contacts close against each other to prevent this, but I know from experience (with elevator controls where this is a big problem*) that the C-H side mounted aux contacts don't have that wiping action (Siemens too). This is especially bad on machinery where there ends up being a lot of vaporized oil and/or coolant in the air (hence the issue with elevators). They do have it on their top mounted aux contacts, but on Size 3 and up they don't offer the top mounted aux. The only viable solution I found was to just change out the aux contacts periodically, or instead of going through that aux. relay, just switch whatever the load is directly.
* The reason I know this is because I once got paid to do an in-depth study of why aux. contacts on Siemens starters kept failing in the elevator industry. It was happening on Siemens and C-H, but not other brands. Of the brands this one company used, those two did not have a wiping action, and on C-H, that was only on the side mounted aux contacts, which they only used on Size 3 and 4.