Should I be reducing salt amounts in recipes if cooking with tap water that has passed through a salt based water softener?

No

Water softeners do not add any salt to the water. They use the sodium from the salt, not the salt itself.

This is known as an ion-exchange process

If your softened water tastes at all salty, you need to check with a maintenance engineer.

In 'health' terms, there is a slightly increased sodium content, but in flavour terms there is no additional salt.