It depends on the dog. I have a foster right now that can't be around the small animals. He whines, barks, jumps on cages... and he's like 100lbs. He is improving but I keep him leashed and tied to something as well as me holding the excess so he can't get close enough to the cages. My other dogs that I raised I don't worry about too much. The shiba would kill them given the chance but she's too scared of getting in trouble and too small to open doors so we just have to keep them separated and supervised. My akita loves small animals and must tell me when there are babies. She follows me in to the blocked off areas with the cages. The husky puppy is learning quickly. She sometimes thinks she needs to be involved with the handling of small animals. Especially if people come over and are paying attention to them. I have to keep reminding her not to jump at the animals.
In all cases, no matter how good the dog is, we do not rely on just the cage. I have seen on here and other forums where dogs who were always good with the guinea pigs just ripped the c&c cages open one day. Zipties will only stop very small dogs if they are determined. When we are gone the dogs are in crates and all small animals are behind a solid door or we do have some chinchillas in very very sturdy cages that we don't always close the doors to the rooms. If we are home we know where the dogs are though and can hear if anything exciting is going on. The foster is doubly separated by having his own room so he'd have to break out of his solid hardwood door, break in to a solid hardwood door, and break in to a cage. I still worry.
There was an incident where my akita opened her crate (I have no idea how since it has the spring latch on the outside that we reinforced with wire after the last crate died), opened the room door, unlocked the basement door (again, how?), opened the basement door, got through the pen gate, and was partially standing in the cage licking the guinea pigs. I heard odd "wheeeek" *silence* "wheeeeek" *silence* .... I thought those are weird guinea pig sounds. I found them a bit spiky furred but unharmed. What do you do with a dog like that? She can even turn bolt locks and open the door. If you use a key she will take the frame off over the area of the lock and chew out the wall. We find her waiting on the porch for us about once every 6 months cause she got bored in her crate.