TRACON Controller described loss of separation event when facility point out procedures to another sector were not followed by a fellow controller; reporter noted the infraction; issued corrective turns; but not in time to secure required separation.

Narrative

I was working the east arrival position and granted a point out to the East Departure Controller to use part of my airspace to climb a departing aircraft. Normal procedures for this type of point out is to issue a vector to get the departure out of the arrival corridor quickly to avoid any conflicts with an arrival. The Departure Controller failed to do this so I issued a vector to my aircraft to avoid losing separation. It appeared separation was going to be lost so I issued another vector. He stated he was turning and had the traffic in sight. I instructed him to maintain visual separation but after tape review; it was revealed that separation was already lost. After reviewing the voice recordings and track plots it was revealed that my aircraft NEVER turned the airplane until after I turned him the second time; 23 SECONDS later. Had the pilot turned when I first instructed him separation would never have been lost. The facility failed to file a pilot deviation for unknown reasons.