I don’t know whether it’s intentional or not (I haven’t read the event FAQ in detail), but the event progression is tied to the account - not the character.
One of the event tasks is to complete 5 assignments in Vanguard. Completing assignments in Vanguard will progress the event and add event points in EVE. Those points are applied on all characters of the account that is playing Vanguard. In bullet points:
- Log in to Vanguard and complete 5 assignments.
- Log in to your EVE account that played Vanguard and claim event points on all 3 characters on the account.
- Rinse and repeat.
To CCP: If this was not an intentional feature to incentivize players to test Vanguard and the integration between two games, please respond here.