Let me copy some potential useful information we released when the feature was launched because I’m not sure if this is well documented:
A new parameter, primary_web_event_tag, has been added to POST /0/accounts/:account_id/line_items which will allow for the setting of this value. The value can be retrieved on GET /0/accounts/:account_id/line_items and GET /0/accounts/:account_id/line_items/:line_item_id.
Note there are no changes to the PUT endpoint, once this value is set on a line_item it cannot be changed via the API or UI.
This change does not directly affect any stats reporting but will have an affect of conversions being more accurately attributed to the desired line_items, aggregated data will not change.
In the UI at ads.twitter.com advertisers will see conversion data for the primary web event tag associated to a campaign initially and must click on the detail pane in order to see conversions for all tags. In order to replicate this behavior in your own UI you can segment stats data for a line_item on the primary_web_event_tag ID for that line_item and display that separately from the total conversions for that line_item.