That should be all that is needed there ...

Then, make sure you have the right setting for Configuration ... My Store ... where the default is usually Shipping
Basis of Product Tax
On what basis is Product Tax calculated. Options are
Shipping - Based on customers Shipping Address
Billing Based on customers Billing address
Store - Based on Store address if Billing/Shipping Zone equals Store zone

Shipping
Billing
Store
and for this one, default usually Shipping:
Basis of Shipping Tax
On what basis is Shipping Tax calculated. Options are
Shipping - Based on customers Shipping Address
Billing Based on customers Billing address
Store - Based on Store address if Billing/Shipping Zone equals Store zone - Can be overriden by correctly written Shipping Module

Shipping
Billing
Store
and make sure this is set to OFF or false:
Display Prices with Tax
Display prices with tax included (true) or add the tax at the end (false)

true
false