Here are different scenarios to explain how conversations could appear as glitching:

Why there are incoming calls from different people all being attributed to the same number (e.g. +266696687)?

When Calls from multiple contacts are merging into a single contact/conversation, it is because the leads are calling anonymously.

More information: Why am I getting calls from these strange numbers?

Why you are seeing replies in separate conversations

If you notice that there are multiple conversations going on about the same topic, it is because your Twilio number is added to a group conversation.

Right now we don't support group Group Texting/ Group SMS, please vote up here so we can enable the ability to text in a group: