You really need to look at breed instincts if you want an indoor dog with your chinchillas. I am not familiar with the breed you are looking at but I know terriers and chihuahuas do not go good with chinchillas - from experince. I would get your puppy in there with the cages from day one to get it used to them, but I would never trust a dog with them when the cage door is open.
We just got a blood hound a few weeks ago. Big responsibility! He is already very good with house training but we have to get up with him all through the night. It is like having an infant. He is 13 weeks old now and we have finally gotten it down to walking him at midnight, 3:30 am, and 6 am. He can hold his bladder well for that amount of time. We are exhausted though!
My chinchillas have their own building outside of the house but I do take the puppy with me. It took a lot of training to get a strong understanding of the "leave it" and "no bark" commands. Now he is an angel. He will look into the lower cages and eat dropped chinchilla feed from the floor but he will not bark or jump on the cages and will immediately back away and sit if I say "leave it" in a normal voice.