Precursive Board organization-wide default sharing settings are Private with Access Granted Using Hierarchies enabled by default - only the owner and team members on the Board will see the Board. 

When Grant Access Using Hierarchies is enabled, users above the Board owner in the role hierarchy will also see their subordinates' Boards. 

Precursive Tasks are Controlled by Parent - their visibility and access are controlled by the default sharing settings in Lists, which are controlled by the Precursive Board. Therefore, in order to see other people's Tasks, you need to see the Board that contains those tasks. 

This also means that you won't see any Tasks or Boards where you are not the Owner or are not part of as a Team Member (Board Team Members).

How can I see my team's Boards if I'm not a member?

It is possible to extend visibility and access to the Board and its Tasks in three ways:

1. Add or Remove a Board Team Member (Read/Write) 
2. Manually Sharing the Board (Read-only or Read/Write)
3. Defining Sharing Rules  (Read-only or Read/Write)

Note: You can only share Taskfeed Boards to users who have a Precursive licence assigned (Assign a Taskfeed License to Users).

1. Adding Board Team Members

Board Team Members are people added to the Board through the Contributor button on the Board itself. Contributors will be listed at the top of the Board so they can be dragged onto a Task to assign ownership.

2. Manually Sharing the Board (Salesforce Classic)

This feature is provided by Salesforce. Go to the Board record via the Precursive Board tab. The owner of the Board can manually share the Board to users in Salesforce or Public Groups defined by the Salesforce Admin. 

Troubleshooting: Why can't I see the Sharing button on a Board record?

3. Defining Sharing Rules

Board sharing can be defined for an entire set of users in a Public Group via Precursive Board Sharing Rules. 
Sharing Rules are created by the Salesforce Admin and can be based on Ownership or Criteria, such as field values.