New faucet, rusty water?
good or bad I will not say, but is normal for old pipes.
What happens is, when you turn off the water to do the change.
Old sediment in the pipes is relaxed and disturbed.
Now when you turn the water back on, the sudden pressure disturbs it more.
Sometimes is sediment that will be disturbed and actually get stuck in the new valve stopping it from closing all the way, causing a leaky faucet. May actually need to manually remove it.
Is nothing new or different in your old pipes, just turning the water off to be able to work on the new valve, then turn it back on, disturbs what is already in your pipes.
It will clear out and be like it was.
How can you avoid it?
Repipe the whole house for thousands of dollars. Or just let the water run and will clear itself out.
If it was easy, we would not call it work!