If you have multiple connections to different webshops, you should use the multiple Sales Channel functionality to synchronize customers.
You can find it here in BC:
Sales & Order Processing | Sales | Customers by Sales Channel
Per Sales Channel you can add an entry. To synchronize to the web, check the field 'Publish to Webshop'. For batch inserting records in this table, ue the function 'Insert Customers by Sales Channel'.
To activate this functionality, you should activate the appropriate messages in the Synchronisation Dashboards.