This recipe is listed under the section for fermentation, together with beer, wine and mead. The section starts with the sentence "Wine, beer and traditional sodas all depend on yeast to ferment sugar into alcohol and generate carbonation".
I don't know enough about the history of soda to know if early sodas were alcoholic. Or rather, I am quite sure that there were alcoholic, fermented, carbonated drinks long before what we call "soda" today existed, but I don't know if they were called soda.
Whatever the language problem is, this recipe is definitely intended to produce a low-alcohol beverage, comparable to beer. If you want carbonated syrup, you should buy a carbonating machine. These take a bullet full of CO2 and press it into the drink base you have selected.
As for the too-strong carbonation, this is probably due to the vague term "room temperature". Yeast growth speed depends on temperature. Because it is an exponential growth, even small changes in temperature can lead to vastly different results. If you want to repeat the experiment despite the alcohol production, try better controlling for the temperature. As I don't brew, I can't tell you the temperature for optimal carbonation after two days, you will have to find it out by yourself.
This is not really an answer,
but rather a report on an experiment.
After the discussion here I got very curious and wanted to compare what I would call a "yeast cake" (even though this is against the traditional definition, but the texture is more or less that of a spongy cake/quick bread) to the "same" cake made with baking powder.
To perform the comparison I divided all ingredients in two and the only difference between them was the leavening.
I tried to keep it really simple, and threw together some ingredients that I had in the house (using a simple quick-bread/muffin method).
Just so you have the feeling of what the batter was like, I will add my experimental
materials:
For each cake I used:
2 ¼ cups soy milk
¾ cup baking margarine
3 cups all-purpose flour (type 550)
2 cups raw sugar
¼ cup cornstarch
½ tsp ground vanilla pods
Then for one (A) I added:
1 ½ tsp dry yeast
2 tbsp sugar
and for the other one (B) I used:
1 tsp baking powder
½ tsp baking soda
2 tbsp cider vinegar
For both I warmed up the milk and margarine just enough that it melted and added the vanilla, then let it cool down.
For A I then added the extra 2 tbsp of sugar and the yeast, and let the yeast get activated and work for an hour - the soy milk curdled and completely separated. When I made B I added the vinegar to the milk mixture and mixed - the soy milk got thicker and curdled a little. The baking powder and baking soda I added to the dry ingredients.
After waiting for an hour for A to do its thing (of course B was ready to put in the oven instantly), I poured the milk mixture into the combined dry ingredients and gently stirred, just enough for the components to combine. I poured the batters into oiled and floured pans and baked each cake on its own in a preheated oven for 40 minutes (this is when both passed the skewer test) at 350 F.
Results:
Both cakes rose to 2.5 times the batter height/level. However, B rose more evenly, whereas A rose a bit less towards the edge of the pan. B smelled like a normal cake/quick-bread, but A filled the house with a "doughnuty" smell (the most scientific term that can be used here would probably be: super yummy). When cooled and cut, both had a really (equally) nice bouncy, fluffy, slightly crumbly spongy texture. A had a bit more and larger trapped bubbles, see figures 1 and 2.
One of my taste testers (or is it test tasters) is quite sensitive to baking powder, and said B tasted a bit too much like baking powder. Everyone agreed that A tested a bit more complex. Both cakes would probably have been better with some nuts or chocolate or fruit, but I avoided these in order to have less complex experimental conditions, to make the cakes easier to compare.
Fig. 1: Side-by-side comparison of the yeast leavened "cake" (left) and the baking powder leavened cake (right).
Fig. 2: Zoomed in image of the yeast leavened "cake" (left) and the baking powder leavened cake (right).
The experiment was performed using an electric oven as I don't have a bread machine. A comparison between this two would be interesting as well.
Best Answer
I agree with @SAJ14SAJ. What I would add is that
yeast does not require sunlight in any way ... but as UV light can be harmful to microorganisms and might inhibit yeast growth I wouldn't brew it in direct sun.
for bottling beer it is normally suggested to leave the correct amount (1 - 1 ½ inch) of headspace (air) at the top of the bottle for carbonation and proper pressure. But I am not sure if the same conditions apply for soda - I would think it is not too different.
shaking gently occasionally might help to evenly distribute the yeast in the sugar solution, and expose it to more food resources (sugar).