Date: 201506
Local time of day: 1801-2400
Location: ZKC.ARTCC, KS
Aircraft: Small Transport; Low Wing; 2 Turboprop Eng
Flight plan: IFR
Flight phase: Initial Climb
Airspace: Class E ZKC
ATC / advisory: Center ZKC
Second aircraft: Small Aircraft; Low Wing; 1 Eng; Retractable Gear
Reporter organization: Government
Reporter function: Instructor; Enroute
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Training / Qualification; Time Pressure; Distraction; Communication Breakdown
Second reporter function: Trainee; Enroute
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Contributing factors: Human Factors; Procedure
Primary problem: Procedure

Narrative: I was OJTI on the R-side with a trainee. It was the first day back from weekend and within 30 mins of the beginning of our shift. Traffic; WX; radios; etc. was not a factor with the exception of a terrible understanding of the rules/responsibility of the trainee/tower; by the trainee; during the application of visual separation between an arrival and a departure. Aircraft Y was inbound to GCK for runway 17 approximately 7nm due east of the field with the runway airport in sight cleared for the visual approach and I believe switched to tower frequency. Tower then calls and requests release on Aircraft X off runway 17 and offers to provide visual separation. Without any hesitation; the trainee approves the call and releases Aircraft X. Simultaneously; I got up out of my chair from behind/adjacent the trainee to see for myself where Aircraft X was headed which was on course to ARV which I had no idea where it was at. Immediately; I asked the trainee where this airport was and he responded to the north/northeast. A discussion quickly ensued about whether or not this was acceptable since the tower was providing visual separation. This happened so quickly; I didn't have a chance to stop it before we hung up with GCK tower. However; I quickly figured out where this destination was and I could have prevented this by calling back to the tower. I went against my better judgement by not doing this wanting my trainee to rise to the occasion to fix the situation he created not knowing at the time he didn't understand that the tower is providing visual to get the aircraft off the ground but 'doesn't care' after he's in the air and that it's our job as radar controllers to ensure separation after the departure phase. I wanted the trainee to see and work through the mess he created. After departure; Aircraft X flew right towards the inbound Aircraft Y of course; the trainee simply watched the situation before I keyed up to turn the Aircraft X 20R. Separation had been lost at that point and trainee did not perform as expected. I take full responsibility of the loss of separation and wish I would have handled this differently. I definitely learned something as a relatively new OJTI in how far to let a trainee go. Although I was just filling in as an instructor and only trained this trainee 2-3 times now; I wish I would have had a better understanding of the knowledge of this trainee. Although I never would have guessed at this stage in his training; in his mind; visual separation takes care of everything.


Second narrative: Aircraft Y Was inbound from the east for a visual approach to GCK; reported the field in sight and was issued a clearance for the visual approach. He was then switched to GCK tower and radar service was terminated. Very shortly after GCK Tower called and requested a release for Aircraft Y for an on course departure to the north east offering to provide visual separation. I issued the visual separation phraseology and hung up. The tower released Aircraft X almost right away and in his climb came within 2 miles of Aircraft Y.It was my understanding from training that the Tower was responsible for separating the aircraft by ensuring they can visually maintain separation. I don't know how they thought they could visually maintain separation in the manner they applied it. I was told that I was wrong in my interpretation and that they only care about getting the aircraft off the ground and that as long as they had the separation they needed leaving their airspace that they didn't care about the rest. I should have issued a heading with the approval for visual separation which is what I will do in the future to ensure that something like this doesn't happen again.


Synopsis: ZKC Developmental Controller releases an aircraft from a Tower controlled airport and instructs the Tower to use visual separation. Aircraft comes onto ZKC Controller's radio and Controller is confused on how the Tower provided the use of visual separation.