Would a return label printed at the time of drop-off at a UPS store have an issue with the package coming back to me?

I had to drop off a few documents and also include a return label inside the envelope for the receiver to send another envelope back to me after processing my documents. I printed both the labels at the UPS store during my drop off time, applied the label with the receiver as the destination on the envelope and just put the label with my house as the destination inside the envelope with the other documents so that the receiver can just stick it onto the envelope on its way back. Those documents are very important and I’ve set them to go by 2nd day air.

It’s been 2 days since then but just out of curiosity, I checked the tracking on the return label and it shows “package received” at the facility near me when it shouldn’t have. Would that be an issue when the person on the other end tries to drop off the return package with the label that I sent him?