If you want to sync bills in a currency that's different to your accounting currency in QuickBooks Online, you first have to activate multicurrency support in your accounting software and assign currencies to vendors.
Enabling multicurrency in QuickBooks Online
Here's how to enable multicurrency in QuickBooks Online:
Open QuickBooks Online
Open the Settings wheel
Click Account and settings → Advanced
Scroll down to Currency
Toggle Multicurrency
Enabling multicurrency in QuickBooks Online can't be undone. If you're not sure if this is the right setting for you, consult with your accountant first.
Adding a currency to a vendor
Once multicurrency is enabled, QuickBooks Online allows you to add a currency when creating new vendors.
Matching vendors per currency between Request Finance and QuickBooks Online
Once you've added your vendors in QuickBooks Online with their respective currencies, make sure to match them against vendors in Request for the sync to work by following the steps here.
QuickBooks Online does not support having a vendor with the same name. If you receive payables in different currencies from the same vendor, you need to duplicate the vendor (once per currency) in both platforms, Request Finance and in QuickBooks Online.
For if the vendor "ACME Ltd." sends you bills in USD and EUR, then make sure you add them twice in both platforms. For example, add "ACME Ltd. (USD)" and "ACME Ltd. (EUR)" in both platforms.