Earn Income is not the Perform action, so you can't use Acrobatic Performer when Earning Income
You've quoted Acrobatic Performer which only lets you replace Performance with Acrobatics if you use the Perform action. But looking at Performance, we can see that "Earn Income" is a "Performance Trained Action" while "Perform" is its own specific action. Thus you cannot replace the Performance check from Earn Income with Acrobatics using Acrobatic Performer. That said, a GM is certainly allowed to simply let you do so anyway; it is a performance after all.
Your GM can just let you use Acrobatics instead of Performance anyway
The rules on Earning Income state (emphasis mine):
You can use a skill—typically Crafting, Lore, or Performance—to earn money during downtime. [...]
[...] In some cases, the GM might let you use a different skill to Earn Income through specialized work. [...] such as using Acrobatics to perform feats in a circus [...] If you’re using a skill other than Crafting, Lore, or Performance, the DC tends to be significantly higher.
It is going to be up to the GM to determine whether they actually let you use Acrobatics in this way, and also whether that makes the DC any higher at all; but it is an option as well.