Why is it that if you tick the box for tax to be included in the product/unit price shopify seems to change the tax rate? For example NZ GST is 15%, however if the 'include in price' box is ticked, shopify shows taxes equal to a rate 13.04%. If however you use the option of adding taxes at checkout it uses the correct tax rate. Why the difference?
Am answering this as I understood you issue. Seems like you have to adjust your Product base price to correctly calculate tax like you want.
Attached is a sample screenshot with two orders - one with a tax inclusive and other with exclusive. I have adjusted the price of 'exclusive tax product' to get the same calculated tax in both cases. Hope it helps.
If this doesn't help reply with a screenshot of your order where you see the miscalculated tax. Will be glad to help.