Welcome! Good for you for thinking about your riding and most especially for getting training.
At the speeds you're talking about, it's countersteering. Direct steering (i.e. consciously turn the bars left to go left) really happens only at walking pace. Even then, you're actually countersteering a teeny tiny bit to get the bike leaned... you just can't feel it.
You'll use direct steering on the dreaded MSF "box" drill. Watch this... it shows the kind of speed where direct steering makes sense:
Link to original page on YouTube.
There are two super-important things to always keep in mind, but most especially on those low-speed turns.
1) Look where you're going, not at the ground right in front of the bike. You go where you look. Look down, go down. It works for steering horses, and it works with humans. Lift your vision and look at the corner exit.
2) Roll on the throttle through the turn, always. That does not mean pin it. It means that (pretend I'm Keith Code for a moment) once the throttle is cracked open, it is rolled on smoothly and continuously throughout the remainder of the turn. You may wind up at only 1/4 throttle by the end, but you started from closed throttle.
A really common newbie mistake is to lay the bike down on one of those low-speed corners, and the reason is usually because they didn't twist the throttle. They slowed down, leaned over for the corner and the bike just fell. In 28 years of riding I've crashed only once, and that was why. I was going maybe 10-15 mph at the time. It was when I had about as much riding experience as you do now.
Watch the rest of Twist of the Wrist. A lot of it is more advanced stuff for the track, but it absolutely applies to the street. Read the book, too. I also highly recommend David Hough's Proficient Motorcycling, and Ken Condon's Riding in the Zone is pretty good as well... it also comes with a DVD full of parking lot drills.