there is nothing Like when to do white box testing because 
according to me depending on  nature of project  under 
development , depending on analysis at begining stage 
testing methodology is selected either as white box/black 
box testing.mostly white box testing is applied for the 
testing process carried with internal knowledge of system 
for this type of testing tester should have the knowledge 
of programming on which the present system  been developed.

more importantly there is not only the developer but also 
testing people will do the white box testing , the one who 
does the white box testing are called as white box testers

ex: Embeded Testig,protocol testing etc 

i hope this will answers your question...!

                                      regards
                                         ravi

white=box is a technique for testing any application it is 
done in development environment by developer.whitebox 
testing is done only for internal coding.best example is 
unit testing,link integration testing

White Box is technique of testing. Unit and Integration 
testings are come under the white box testing. White Box 
testing is completed by develovers and as well as white box 
testers. In this testing need to test internal logic like 
Path, Loop, Statement etc.

White box testing is technique used for testing.It requires 
internal knowledge of code/system.test technique will be 
decided on the basis of type of project and through 
analysis.eg. for testing of safety critical 
software,complex software.It can be done at different level 
(Unit to user acceptance testing).In unit and integration   
testing white box testing will be performed by devloper.In  
system testing it will be performed by independent test 
team and user acceptance testing is performed by tester.It 
also depends on organization.After performing black box 
testing (specification based) white box testing is 
performed to assess the percentage of code coverage and 
then to design the additional test cases to meet the 
desired coverage.

White box testing is fully based upon source code of program.Tester also will do white box testing.But if the testing is functionality vise,black box testing will be involved.If the tester will do both,white box and black box testing will be involved.