How do I Stop customer from browsing projects

[Matt Smith]

I have created the Project (Customer Specific) [a].

I have set the project permissions to "customers who are added to the project"

The customer only has "Service Desk Customers" permission to project [a].

I am confused as to how he can browse and raise tickets on other projects (customer specific) from the customer portal when he views all requests. also on the landing page of the portal.

[Nic Brough -Adaptavist-]

It sounds like you have given your customer a full Jira account instead of just a customer account.  Try removing them from the groups that grant access to Jira (you can see these under "manage applications")