I suspect there isn't one way that fits here all, but I can tell you my experience.

My trading account is denominated in USD but on two different occasions now I have traded EUR dominated futures contracts. When this happens my account shows a USD balance, a EUR balance and a combined balance which in my case converts the EUR balance to USD at current fx rates. initially your non-base currency balance (in my case the EUR) will be negative because of the margin requirement. When it's negative, your broker will probably charge you a funding rate, even though you have a positive balance in your base currency and they aren't paying you interest on that! The alternative is to deposit funds in the other currency, something my brokers would allow me to exchange through them. For what its worth I did NOT do that, as at the time interest rates on the EUR were negative and my broker would have charged me for having a positive balance! At the end of the trade I had a EUR balance and my broker (when requested) just converted that to USD at the prevailing rate.

To be honest it was messy and is one of the reasons I don't trade non-USD denominated contracts anymore.