Your Quai wallet's address belongs to one of 9 zones on the Quai network. While processing of transactions is isolated between zones, it's possible to send assets from one zone to another. You don't have to worry or do anything special in this case. Simply enter the destination address and amount. Koala Wallet will take care of figuring out if the zone is different or not, and handle everything automatically. You can read more about Quai's shard hierarchy here.
Diagram of shard hierarchy and transactions in the same zone, intra-region and inter-region
Transactions to and from the same zone complete within seconds.
Transactions to a different zone in the same region must first be included in that region's controller shard before confirming at the destination. This add fees and confirmation time.
Sending to a different region requires the transaction to be included in the Prime shard before it travels again down the hierarchy to the destination zone. It takes longer for such transactions to confirm.
In any case, as stated, this entire process is automatic. Any multi-stage transaction requires no special action from the sender. If your transaction is taking longer than expected to confirm, most likely it's cross-zone, so please be patient.
If the transaction hasn't confirmed after more than 2 hours, a technical problem may have occurred. In this case please open a support ticket explaining the issue and including the transaction ID and involved addresses so we can check.