E pass minimum salary

No, your employer or you may read wrongly, minimum salary limit is remaining same $3,600 (eligible to apply EP), but they increased salary limit to $6,000 allow you to bring your spouse and family here.

The minimum salary of S$3600/month to get an EP applies to fresh graduates - experienced or higher educated applicants need a higher pay (in line with their market value) to be eligible.
So it might well be that S$6000/month is the threshold for you - but MoM purposely keeps their criteria confidential and (as far as I know) also doesn't openly talk to companies about it, so your agent's claim is dubious (agents are known to be often less than honest).

Thanks Surya