Yes, an organization selector field would be ideal but it wasn’t necessary at the time of building this and adds a lot more complexity. It may be something I try to introduce at some point but this is the first request for that feature so far.
Basically what happens is when you enter your private token, that token is used to fetch the account’s first attached organization. Then it will use that organization ID to get all their events.
So if your account has multiple organizations you will only be able to get the first one & would need to get the private token for the account in which the organization was first created with.
Hope that helps / makes sense.