[SalesForce] “Methods defined as TestMethod do not support Web service callouts” error when testing apex callout

I am trying to write a test for a trigger that is firing a future apex callout :

The trigger calls the callBillingService method from this class:

public class BillingCalloutService {
    //Implement business and callout logic methods here
    @Future(callout=true)
    public static void callBillingService(List<Id> recordIds) {
        List<Project__c> projects = [Select Id, ProjectRef__c,Billable_Amount__c from Project__c Where Id = :recordIds];

        List<Project__c> projectsToUpdate = new List<Project__c>();

        String username = ServiceCredentials__c.getValues('BillingServiceCredential').Username__c;
        String password = ServiceCredentials__c.getValues('BillingServiceCredential').Password__c;

        String auth = username + ':' + password;
        String encodedAuth = EncodingUtil.base64Encode(Blob.valueOf(auth));

        for(Project__c p : projects) {

            BillingServiceProxy.InvoicesPortSoap11 service = new BillingServiceProxy.InvoicesPortSoap11();
            service.inputHttpHeaders_x = new Map<String, String>();
            service.inputHttpHeaders_x.put('Authorization', 'Basic ' + encodedAuth);

            BillingServiceProxy.project project = new BillingServiceProxy.project();
            project.username = username;
            project.password = password;
            project.projectRef = p.ProjectRef__c;
            project.billAmount = p.Billable_Amount__c;

            if(service.billProject(project).equals('ok')){
                projectsToUpdate.add(new Project__c(ProjectRef__c = p.ProjectRef__c, Status__c = 'Billed'));
            }
        }
        shouldIRun.stopTrigger();
        upsert projectsToUpdate ProjectRef__c;
    }
}

Error

Methods defined as TestMethod do not support Web service callouts

Test Class

@IsTest
private class BillingCalloutServiceTest {

    @IsTest
    private static void testBillingCalloutService() {
    Account a = new Account(Name = 'Acme');
    insert a;
    Opportunity o = new Opportunity(Name='Test', StageName='Submitted Project', AccountId=a.Id, Amount=1000, CloseDate=Date.Today());
    insert o;
    Project__c p = new Project__c(Status__c='Running',Start_Date__c=Date.Today(),End_Date__c=Date.Today(),Billable_Amount__c=10000,ProjectRef__c='projectX',Opportunity__c=o.Id);
    insert p;

    insert new ServiceCredentials__c(Name='BillingServiceCredential',Username__c='toto', Password__c='azerty');

    Test.startTest();
    Test.setMock(HttpCalloutMock.class, new BillingCalloutServiceMock());
      p.Status__c = 'Billable';
      update p;
    Test.stopTest();
    // runs callout and check results
    p = [select Status__c from Project__c where id =: p.id];
    System.assertEquals('Billed', p.Status__c);
    }

}