There are various ways to invite new members, for example through the Setting (⚙️) menu Invite People.

Inviting

When selecting 'Invite people' new people can be invited by entering their email address, as well as granting access to additional Spaces, for example Private Spaces.

When entering an email address or a name, once the value is correct, a drop down box will appear below the text field:

You must click on this box to add the person to the list of invites. If you don't click on it, the person / email address will not be invited.

Space Access

When inviting new members to an organisation, they will automatically have access to all your Organisation's open and public Spaces.

The list of open and public Spaces are shown. If you'd like to add private Spaces, you can click on the link "...give them access to additional spaces" and a selection box will appear where you can type in the name of private Spaces or select from the drop down.