Using the relationships and portals you've defined only work to link existing Person and Event records to each other in the eventJoin portal. To cretae a new person record or a new event record, you'd need to add a button and script to create the needed new, blank records.
Here's a new person record that you could perform from a button on your event layout:
Set Variable [$EventID ; Value: Event::Event_ID]
Go To Layout [Person]
Set Variable [$PersonID ; Value: Person::Person_ID]
Go To layout [EventJoin]
Set Field [EventJoin::Event_ID ; $EventID]
Set Field [EventJoin::Person_ID ; $PersonID]
Go To Layout [original layout]
Note: to link existing persons to the eventJoin portal, you need to add the EventJoin::PersonID field to the portal and format it as a drop down list or pop up menu listing the PersonID's and Names from the Person table.
In the Manage|Database| Relationship tab if you double click the relationship you will see check boxes near the bottom that say Allow Creation of Records via this relationship. If you check those (both since you want to create records either way) and add scroll bars to your portals you shouldnt have problems.
Phil may be by and tell you that you should create table occurances and check only one side of the relationship in order to ensure that the functionality you want is present only on the layouts you want it on. (Id agree)
Not meaning to speak for Phil. :)