btw, it's a nice tank and it looks good - a good start.
The plants consume the ammonia before it goes any further down the Nitrogen cycle, and the nitrifying bacteria drops in as it finds any ammonia and nitrite which end up as nitrates. Assuming there's enough light for the plants to photosynthesize. In any case, whether you're a plant or a bacterium, it's very important to have good water circulation to distribute the oxygen, carbon dioxide, and nutrients (including ammonia) around the tank.
A Silent Cycled Tank
MY 10 GALLON PLANTED TANK:
2 x 10W CFL; Fluval U2 internal filter; MGOCPM/black sand cap