I could read this question more than one way. Are you talking about an enzyme in a cell or in a reaction in vitro? Kinetics and mechanical explanations can overlap, but are not entirely the same and are usually dealt with separately - kinetics with watching the rate of reactions in a tube and mechanism in a crystal structure or possibly Nuclear Magnetic Resonance.
Protein structures are usually static- you only get a time lapse snapshot of the reaction in most cases. kinetics allows you to see how fast these things go and can help you understand the order of binding when more than one component is needed for the reaction, etc.
The polymerase has a binding pocket where the template strand and the growing strand are used to build a double helix together. if the base being introduced does not form Watson Crick base pair bonds, the geometry of the reaction will not allow the base to be added to the growing strand.
Hope this helps? If I can make this clearer, can you drop me a comment and I'll revise...