Bum hanging off the front edge is normal for hardshell seats. Those mesh ones are ostensibly more chair-like, but the same principles apply: Don't worry about where your bum ends up, the important bit is your spine - you're aiming for your lower back to be well supported somewhere in the middle of the seat, with something for your shoulders to push back against. The pedals will take care of the rest.
What you'll find will probably happen is that over the first 20 minutes or so of continuous riding, you end up slumping into a slightly different position from when you started, and staying there. *This* is the position that you want to sort your bike fit out for, wriggling back into some other position isn't going to work long-term.