Who pays for plumbing?
In general, a broken handle on a shut-off valve is a STRONG indicator that the valve needs to be replaced - otherwise the original handle would not have broken. Replacing a handle on a valve that requires so much force to operate that the handle breaks is not good workmanship, and does not solve the problem of an inoperable shutoff.
If the one was bad (sounds like a fixture hot - cold pair, but you didn't say) it's commonly the case that the other one is as well.
So, you pay the plumber. You might ask questions, but you pay the plumber.
If you are upset about a fairly normal &quot;you see this problem (a handle) the plumber sees that problem (a pair of valves that are failing or failed)&quot; then be immediately available when the plumber is working to discuss changes in scope and why they are being changed. And be very clear that you want to discuss any changes in scope beforehand.
This time, you pay the plumber.