HP,
If it was yesterday morning you'd be really impressed if you knew what the police heli was up to on this particular occasion!
You would have been talking to the tower at that point on the approach so I can't really comment for them, but I'd expect them to do similar to the radar controllers.
I'd expect, and teach, that the first thing to say if you're going to break off traffic on the final approach is give a quick pre-amble to the a/c that you're going to have to break it off the approach then "stop your descent, climb to altitude x" then either once that is read back or at the same time follow it up with any heading instructions.
The climb altitude will usually be to 3,000ft to start with unless there are traffic reasons for it to be otherwise.
The break off direction will usually be to the north from the north runway or to the south from the south runway though, as you found, if other traffic is in the way it may not be!
If it's one a/c being broken off it's fairly straightforward, if it's more than one as was the case with this heli then it can be a bit more complicated, especially if you can't turn in all directions.
But in short, yes, turn and climb when breaking off the approach inside 10nm should be pretty much co-incidental.