Sim card conflicts- switching iphones

I got an iPhone X last week, replacing my 5S- staying with my same carrier. The Apple Store employee did not ask me to turn off my old 5S during activation and allowed me to keep my old sim card in the 5S. I just used the sim that came with the new X. I had lots of voicemail issues on the new X, with deleted messages playing in place of existing ones, deleted messages continuing to play for several seconds even after I pressed delete. I returned the iPhone X and went back to my 5S.

I had no idea at the time but I have since been told that leaving my old sim card in my old phone may have confused the network and lead to conflicts, such as the voicemail. I had always thought if you activated a new sim card, the old one was no longer active or in danger of causing problems and it didn't matter what you did with it.

Anyone had any experience with this?