Looking over your city, it looks like all your manufactories are relatively low level, so the boost you'll get from a level 1 aureate phoenix will be very small at this stage of the game. For example, your level 7 marble workshop will give an extra 4 marble when you do a 3 hour production, an extra 7 when you do a 9 hour production, and an extra 13 when you do a 1 day production. Likewise, your level 5 silk building will give 4 to 15 extra silk, depending on whether you do a 3hr, 9hr or 1 day production. Considering how tiny these figures are, it's possible you simply didn't notice the change when you collected your goods. If you want to check that you are actually getting something, next time you feed your phoenix click on a manufactory that hasn't finished running yet, or is currently idle, then hover your mouse over any of the text that lists how much goods you're getting. In green text it will tell you how many goods you're getting from other sources, e.g. relic boost, pet boost, etc. If pet boost isn't listed, or says 0, then something isn't working right, but if it is then it'll say something like "Pet Boost: +13".
Because pet food doesn't do much for your aureate phoenix at this stage of the game I would recommend saving it for later, when your manufactories are a bit bigger. In the mean time it will still give you some really great bonuses every second day, such as lots of coins.
If you can manage to upgrade it to level 3, it will also give you 429 elixir, which will be very valuable for you at this stage of the game, since you won't be able to produce any Tier3 goods (gems) until the next chapter. That will allow you to build up a large quantity of these goods early, or even trade it for lots of lower tier goods. *Edit* Ignore that last bit. Turns out it produces Tier1 goods, not Tier3. Still very useful for you, just nowhere near as much as I originally stated.
I hope this helped.