Shopify Pay
Shopify supports a multi-currency checkout in specific regions for specific currencies when you use Shopify Pay (cf. https://www.shopify.com/enterprise/multi-currency).
Third-party apps
Discount Ninja, uses the standard APIs provided by Shopify to prepare a discounted checkout. The app passes the required values (presentment currency) to the checkout to allow Shopify to create the checkout using the currency selected by the visitor. Unfortunately, there is a defect in Shopify's API that causes the checkout to be displayed in the standard currency.
Open issue
Shopify was notified of this issue on October 5th 2019.
As of today, the issue is not yet resolved.
You can read about the issue or contribute to the debate here: