Team member unable to access the Project site in project online

Anil --

From your description, it sounds like your Project Online app admin mistakenly left your Project Online system in SharePoint Permission Mode, which is a huge mistake.  I would strongly recommend that he/she change the system to Project Permission Mode.  After doing this, he/she will then need to add each user to their proper security Groups, based on their usage of the system.  In essence, all of the PMs will need to be added to the Project Managers security group and all of the Team members will need to be added to the Team Members security group.

Once this is done, your PMs will need to open and check out their enterprise projects in Microsoft Project, and republish them.  At this point, team members will automatically be able to access the SharePoint project site for each project in which they are a team member.  Hope this helps.