Simple Invoice just prints your order data as an invoice. Once you have your taxes set up correctly in your Shopify store, Simple Invoice will use these tax settings and automatically display all the required tax details on your invoices.
Do you mark your products as “taxable”? If you didn’t do that, for proper taxation, please check the “Charge tax on this product” checkbox for your products.
Did you set tax rates for each country you make sales properly? If you didn’t do that, for proper taxation, please set a tax rate for each country you make sales.
And It might happen sometimes that a customer was accidentally set as “tax-exempt” when they should not have been. Please also check the customer settings for your customers.
Additional info: Shopify will not automatically update your old orders when you make tax changes. Only your new orders will show the taxes according to your setup.