I don't think there is one accepted way to feed the birds with this method. I don't use the two bucket method, and have read that one of the purposes for the two bucket method is to cut down on the smell when the feed is fermented indoors.
I use a slotted ladle, but before I got the slotted ladle, I just scooped it into the trough with some of the liquid. For the past couple of days, I have been putting fermented feed in the trough, and then I added more water, just to keep everything moist until the birds were ready to eat. (I don't get to the place where the birds live until the afternoon, so sometimes they go to the fermented feed first, sometimes to the sprouted greens, and mostly to their cricket treats. They eat the fermented feed at their leisure, and only eat a little bit at a time, rather than gobbling the whole serving up at once.)
Like sourdough bread starter, as long as you use some of the old culture in the fermented feed liquid or the fermented feed itself, that is all you should need to keep the process going. Sounds like you are doing it exactly right. However, there is the caution not to use chlorinated water because it might kill your culture. I just fill up a bucket and leave it sitting until the chlorination chemicals dissipate, and then use that to replenish the liquid.
The key is that you should get a sour smell. If you get a sweet smell, the fermentation has not gone far enough. You can still feed the birds the sweet smelling feed, you just won't have all the benefits of fermentation.
