How to provide letters of reference for a Postdoc Application
Frequently "reference letter are required to be submitted at the time of application" simply means that "get your letter writers to send their reference letters to e-mail address xxx@yyy.zzz before the submission deadline" (or upload to an appropriate website if the process is more organized). 

This is in contrast to the situation in many faculty hires where the reference letters are solicited: in those situations you provide only the names and contact information of your letter writers and the hiring committee, after sifting through the files to narrow down the choices somewhat, then writes to the candidates' recommenders and ask for letters to be sent 



That said, if you are applying for a PostDoc you are supposed to be young and naive and not know any better, so there's absolutely no harm in writing to the department/head of lab/hiring committee asking for clarification when you are not sure what the expectation is.