I've never worked procedural with real traffic but I've had some simulator years ago. For what I can remember, under no circumstances assigning a vertical speed can influence the separation in a non-radar environment.
Either the routes/tracks are separated or they are not. You may have to cross a certain point at a specified level but, not knowing your exact position, ATC cannot obtain that through a rate but only with a specific restriction (Cross ABC at FLxxx or above/below...).
Same applies if the lateral separation is obtained from/to a radioaid. It should result in a level restriction related to a radial/bearing and distance.
Looks like you've experienced a "let's keep our finger crossed" separation. Not really recommended by ICAO!
Somebody correct me if I'm wrong.