How do remittances physically move money (as opposed to just account balances)?

It doesn’t! (unless of-course you are operating a 100% cash only money transfer network - an example of which I do not know of).

To understand how cash is transferred between countries, read this answer: Faisal Khan's answer to Where do currency exchanges get their currency?

To understand how money transfer works between countries, including remittances, you might want to read these answers that explain the process of inter-country money settlement:

• Faisal Khan's answer to How does a remittance money transfer work? What are all the steps and who is involved?
• Faisal Khan's answer to How does money transfer between banks and different countries work?
• Faisal Khan's answer to How does the settlement of payments work in banks? Specifically, how do payment systems that are connected to multiple banks actually settle the amount between two banks?
• Faisal Khan's answer to Where are countries' bank accounts held?
• Faisal Khan's answer to What exactly happens when money is sent via Western Union versus a company like XOOM? What is the difference?