C172 pilot reported a Low Altitude Alert on approach.

Narrative

I was starting a series of night landings on an unfamiliar runway for night landing currency with no moonlight. City lights and highways are in the vicinity. A strong crosswind blew me much farther away from the runway after takeoff on downwind than I realized. The G1000 was configured to show the ILS for the landing runway. The G1000 ILS CDI often initially shows the runway is behind you when you are still approaching the runway. I don't know at what distance this happens or when it corrects itself; but it is known to flip flop. Traffic was landing on the parallel runway. Since I had been blown farther away from the runway on the downwind than I realized I thought it was taking too long for the CDI to capture and was unsure about trusting it. With traffic landing on the parallel I didn't want to overshoot the runway and cause an incursion with the other plane. I saw a row of lights from a highway I mistook for the runway and started a descent. About the time I saw the approach to the runway I realized I was much too low and started a correction. At the same time the Tower warned me about the low altitude. The subsequent landing was uneventful. My fault for losing situational awareness and good job by the Controller for catching it and issuing a warning. The Instructor for my last flight review said he had also seen the G1000 ILS CDI initially show you had flown through the ILS when it was still in front of you.