Might be wrong, but I believe the background checks are outsourced to firms which specialise in doing that kind of work. Methinks those who got an offer immediately after TT were those who were shortlisted early on due to their educational & internship background (and thus the check was done in advance). Another explanation regarding the speed of processing the background check is that it's been done before for them (e.g. current or previously employed at DBS, like internships).