This is a bit unclear. Here's what's in the rules:
- If you escape from an Assassin, your turn ends. Explicitly stated for his encounter.
- If you have resolved the first encounter on a two encounter spot, you then face the second.
- If Van Helsing escapes from any combat, his turn ends. (pg. 14)
- If you escape from any Agent combat, you cannot face Dracula, and 'your turn is over'. This is under the 'Battling to Reach Dracula' section.
Now, what happens when there is a Minion and another encounter (second minion, new vampire) on the same spot, and you escape from the Minion? If your turn ends in that case too, why is this explicitly stated only for the Assassin? If you would normally continue, on the other hand, then Van Helsing's special rule, as written, is a handicap in this particular situation.
Presonally, it makes the most sense to me that your turn ends when you escape from combat regardless of your enemy. This makes the special entry for the Assassin superfluous, but at least it doesn't introduce headache-inducing exceptions for Dracula and Van Helsing only.