The part design is the culprit. It may on the surface be a simple mould but you can't just put drafts/fillets on and it will work.
Side note - generally speaking you don't do the mould split in the original part file. You probably know that but in case you didn't.
See basic problem at zero draft point = fight of draft vs fillets below.
The problem with the parting surface may be that when you make the parting line, you are asking it to split faces, and it makes an undercut around each of the steps in the PL. At least, that is what it was doing for me. So I turned off the split faces option, and just semi-manually selected the parting line between the fillet and the thickness face, and then it does the parting surface beautifully. It's slightly off because technically the edge of the fillet isn't exactly at the PL when the side faces have draft, but it's pretty close.
I haven't done this in a while, it's actually kind of fun.
Matt I see what you are saying but I think really the OP should look at his part design and understand that it needs fixing.
I'm assuming this is an academic exercise just to see how the tools work.
If this were a real project, you would want to be more deliberate about adding a parting line with draft to both sides, or eliminate the fillet so that the parting surface is coplanar with one face of the part.
You should probably work with your tooling guy to get an idea exactly how to split the part. That's the best way to learn how to design for molding. Of course you get 10 molders in a room, and they'll have 5 different ways to mold the part, but you need to get a feel for what is possible and what is not. The funny parting line the first response shows is caused by the combination of the step in the PL and the fillet. This is why you need to be more deliberate about the PL, plus the fact that the tooling guy is probably going to want more draft around the passing shut off at the PL step.
Designing for plastics processes is a bit of a rabbit hole - it goes as deep as you're willing to follow it.