Hey @vedranilakovac welcome to the Asana Community Forum 
If you create tasks in your private Asana project or a project to which only you have access and nobody else then yes it is correct that only you have full access and other people only have access to the tasks you added them to. More info here Project permissions | Product guide • Asana Product Guide
The team members will however see all tasks also under their “My Tasks” or if you prefer you can set up various projects to which you add team members to and then you can multi-home tasks.
And here is a great post by Bastien on who sees who: Who sees whom, a guide to guest visibility with Batman & Robin