Extra 200/300 Series pilot reported an NMAC event during initial climb. After the flight; the pilot reported the Tower Controller's sequence instructions were given when both aircraft were already airborne and in close proximity.

Narrative

I was cleared for takeoff Runway XX and approved for left turn on departure. The airport is surrounded by rising terrain on all sides. A few seconds after takeoff Tower Controller said 'traffic on left cross wind; follow that traffic'. I responded 'Looking for traffic'. I had already started my left turn at the time of ATC instructions so I stopped the turn on the present heading - approx. 230 - and maintained that heading and climb attitude. I continued the climb due to the rising terrain and because my airplane has a bubble canopy and excellent visibility above - so as long as I could see ahead and above I will not hit the other airplane. My aircraft is also a low wing and has somewhat obstructed downward visibility. During climb in a nose up attitude I did not see the traffic until it had passed underneath me and heading away to my left and by my estimation was at least 500 ft below. Unfortunately; the other pilot was not happy with the situation and made some remarks on the radio to the tower about the event. My thought was that the event was over and that was the end of it. Upon return to the airport I was asked to call the tower via phone - which I did; and learned from the tower manager that the other pilot had complained about the event. The manager was not accusatory toward me; but I did get the sense that the Tower Controllers felt I maybe had done something wrong because I did not pass 'Behind' the other aircraft. I am always trying to learn from situations like these; but I think the sequence events that led to two aircraft being so close together on the pattern started with the takeoff clearance and the towers controller's attempt to correct the error by issuing traffic instructions when the airplanes were already too close together. I can't pass behind any traffic until I see the traffic and that was not possible essentially instantaneously at the time of the tower's instructions.