Pedals revolve backwards when I am off the bike and push it in reverse. The bike has a derailleur. Is there something wrong here?

Nope. If they didn't, you wouldn't be able to go forward by pedalling.

Huh?

With any kind of bike, there's some kind of ratchet or direct-drive so that pedalling normally will cause the chain and rear wheel to move, so if you turn the rear wheel the other way, it must cause the cranks to turn as well. Otherwise it wouldn't work. That's all I was getting at.

OP, your bike is just fine.

My other bike, also has a derailleur, and the pedals don't move when I back it up. With the one that does its pushing the chain the wrong way and that causes problems.

Hmm, does your other bike have a front freewheel crank or something rare like that? This happens with every properly-functioning derailleur bike I've encountered, and I'm curious what "problems" you're experiencing as a result -- let's home in on that.

FFW on the other bike is all I can figure.

BMXers have freecoaster hubs, usually only on nicer trick bikes. I dunno of any made to accept a cassette, however. They have a clutch, so that when pedaling, it engages, but when coasting backwards it does not engage.

If you watch a lot of BMX videos you'll see everyone without a freecoaster has to pedal backwards while they're rolling backwards.

It is a normal bike with crank at the intersection of the normal tubes. I just went and roled it around backward and no problem, earlier the chain seemed to be trying to come off when I backed it up. If it does it again, I will watch and see if I can tell why.

What's the make/model/year of your other bike?

If they didn't, there would be.

Think about it for one minute. If you push the pedals forward they drive the wheel, if you push the pedals backward nothing happens. Likewise, if you push the bike forward nothing happens.

So by logical (and mechanical) extension, the last possibility, pushing the bike backward, would pull the pedals back.

Almost all bikes' chains will try to derail when crosschained even a little bit, while rolling backwards. Derailing while rolling backwards is even more of a problem on some bikes - bikes with bent derailleurs, a misaligned derailleur hanger, or just plain bad luck will derail while rolling backwards even when chain is parallel to bicycle centerline.

I thought the op was saying that when the pedals were moved backward, the bike was driven backward also.

Ah.

That is normal with derailluer bikes if you are cross chained, meaning in a gear that causes the chain to flex from inboard to outboard.
You can lift the rear wheel while rolling backwards, such as getting the bike out of tight storage where you can't roll forwards or turn around..

What if you lift the rear wheel off the ground while going backwards.. That should fix the problem

No, this is not what I meant.

Thanks, I will check that out next time it happens.

The bike is a Soma Saga, with a shimano xt triple.

It's called a sprag unit, or one way clutch. It freewheels one way, and engages when you pedal, so basically pushing a bike backwwrds, the drivetrain pulls aganst the clutch(which is a set of flat spotted roller bearings, or pawls) and engages it. Almost all freewheeling bikes do it. I'd be more worried about the same result forewards.

When you pedal forward, you exert forward force on the rear wheel because the ratcheting pawls in your freewheel or freehub (whichever) engage the gear-teeth inside the FW or FH. When you roll the bike backward, the pawls are still engaged and are now driving the pedals backward. When you are on the bike and it's rolling forward, your pedals can stop rotating and you can coast. That's because the pawls are "slipping" past the gear-teeth, as they are designed to do in a ratcheting system.

Just a different way of saying what others have said.

If you aren't cross-chained, the chain jumping when you spin the rear wheel backward can be due to an insufficiently lubed chain.