While @BDD might be right and I'd consider his suggestion, it's certainly possible that the two tabs are warranted, for all kinds of reasons.
I don't think that the chronological order is a good idea, because the same logic is equally valid for a reverse chronological order. You say that earning comes before spending, but then spending is more recent than earning, so maybe that should be first. In both cases it's a pretty artificial way to order the tabs, and I don't think that users tend to assign chronological importance to the location of tabs.
What you should look at is the usage of the tabs. The difference between them is not just between first and second, it's the difference between having your information in plain sight, and having to perform an action in order to see the information. The income tab is usually a dead end, it doesn't lead anywhere else. The spending tab usually leads to a drill down into the ordered items, delivery status etc. So as you say, it's likely that this is the more important one. I think it should come first.
Regarding the "hybrid" approach - making your default tab not the first one is a very unusual design call, and you need a very compelling reason to do so. It doesn't seem like you have one here.