Hi,
It depends on the address selection mode you are using.
For "list / dropdown" modes, when you edit an address and the same address is selected in the other "side", the other address will be updated in the same time.
When you create a new address, if there is no address before, the two parts will "receive" this new address. Otherwise you will have to select the new created address in the other "side".
The "popup" mode is the "legacy" mode which does not include the auto-update ajax features that the two new modes can propose.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.