Correct all prices must be inclusive VAT.
The app will most likely use the price you set in the product. Prices modified by 3rd party apps will most likely not be used.
So in Shopify > Product > click on your product > the product here or the variant product price is what is used.
If in doubt get in touch with the data feed app support team you use. Not every app is the same and there are hundreds of data feed management tools. All with there unique features.
Im having a similar issue. Google merchant center suspended my account because my webpage shows prices with VAT but the google feed is being sent without VAT because that is how i configured the shopify according to Exempify.
I think that shopify should support VAT rules officially and we should not need an APP for this. Eg: selling to VAT liable customers to not.
You can fix this in Google Merchant Center using feed rules. More info: https://support.google.com/merchants/answer/7450276?hl=en
By adding the tax/vat.
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