Person who pretends to not understand unless one speaks in exactly the words they expect [duplicate]
You could call a person who does that a pedant:
Pedant (noun)
a person who annoys other people by correcting small errors and giving too much attention to minor details; one who unduly emphasizes minutiae in the presentation or use of knowledge (Merriam-Webster)
Your question really poses 2 questions: one where coworkers try to correct you, and one where they pretend not to understand you. The currently chosen answer seems to handle the first question with @Nicole's pedant. However for the second I would submit:
Obtuse
A late answer, and it's a bit radical, but perhaps these people are genuinely trying to help you! Perhaps they seem themselves as friends, mentors, experts or educators.
Sometimes the use of the wrong word is not only confusing for listeners but also a signal that you don't fully understand what you are talking about. Those who deeply understand a domain tend to use language very precisely and can't help notice when others use wrong or loose language. By picking you up on your language, they may be trying to teach you about some distinction you seemingly weren't aware of.
You didn't say exactly what they were picking you up on, so I can't comment on your specific case. It sounds like you consider it something trivial.