Could you explain?

This illustration was created shortly after the American Civil War began, a conflict that started when the South seceded.

Thanks! I think I have the context, but I don't get the joke

The oil wells were in Pennsylvania, which was on the Union side.

So the whales are saying: "May They Never Secede" talking about the wells, in reference to the confederacy whom already seceded. And they say this because obviously if the wells "seceded", humans would go back to whale hunting.

Do I understand it correctly now?

Yes.

it's a joke that has changed meaning over time. Pennsylvania had the oil wells at that time, although given that Standard Oil was founded in 1870 didn't think they were yet so important that one would pray for their success.

The South seceded, along with Texas.

Pennsylvania didn't secede so all good.

But later Pennsylvania didn't have any more oil worth mentioning, but Texas did.

From our viewpoint the joke operates on two levels, that of its time - let's hope Pennsylvania doesn't secede because then we're screwed! And that looking back - Texas did secede and they prayed for the states with the oil not to secede hah hah, irony.

The irony indicating somewhat that usefulness of a resource is time dependent.