Thanks for pointing out this change from how it was with Paypal. What Paypal reported was only the amount transferred from Rover into your account, i.e., what you netted.
However, this new method is actually the way many online business do report. As an example, eBay now reports gross earnings, which includes taxes they collect on your behalf and their fees. Therefore, you have to keep track of all the expenses that can be deducted on Schedule C. My own spreadsheets have columns for the taxes eBay collects, which I don't see at all, both its types of fees and my shipping expenses. Then I make sure that I have marked any transaction that results in a refund. All of these are forms of expense and are deducted from that gross amount being reported to the IRS and your state tax authorities. There are many other expenses that you can deduct, but you'll need to read the Schedule C instructions for ideas.
As Rover's FAQ mentioned sales taxes (not income), that is governed by the state. My own state does not impose any sales tax on services, only goods. However, if your state does, then it will be included in your gross earnings, even though you will never see it, but will deduct it on Schedule C.
As for its impact on your overall tax position, it's a wash. What goes into AGI is the net amount (after you've deducted Rover's fees and accounted for any refunds). It just means you have more record-keeping.