The cart drawer respects whatever currency Shopify reports for the active market.
Shopify Markets
If you use Shopify Markets, the cart auto-shows prices in the buyer's market currency. No special configuration in Oxify required.
Third-party currency switchers
Third-party currency apps work as long as they trigger Shopify's standard currency change. Most modern currency apps do.
How to test
Open your storefront in incognito.
Switch to a non-default market or currency.
Add an item to cart.
Confirm the cart shows prices in the new currency.
If something looks wrong
If your currency switcher uses a non-standard mechanism (e.g. URL parameter only, no event), the cart may not pick up the change. Reach out to support with the currency app name.