“Mirroring” isn’t an insult, or necessarily manipulative. It is literally built in to us humans! Our brains have specific portions dedicated to imitation and empathy called “mirror neurons”.
These neurons help us feel what others around us are feeling. It’s why you feel sad when you see someone else being sad. Or why it can make us smile to see someone else having a great day!
The behavior of mirroring someone is a form of social bonding (“See! I’m like you!”) which is the basis of building human relationships.
Having in-jokes and picking up particular quirks of people around us probably has a special jargon to psychologists.