A carpenter needs exacting precision.
My dog needs exacting attention because she loves to play fetch all day.
Creeping Charlie is a weed that requires exacting patience and persistence.

The boss at my new job was very exacting.

That's not a question, it's a statement. You can agree or disagree with it depending on whether you feel you are exacting in your work. Be prepared not to get the job if you feel you are not exacting and state as much.

Possible answers to "I am exacting in my work."

True.

Yes, quite.

Decidedly.

I take great care to be as thorough as possible.

Exactitude is overrated. (not recommended)

Exacting in work means being very precise, detailed, and demanding in one's expectations and standards for performance. It often involves paying close attention to quality, accuracy, and consistency in tasks and not settling for anything less than perfection.

Be very exacting and accurate.