In scenario you have described you will need only one license.
The component is licensed on per-developer basis. Distribution with your application is royalty free.
As long as each developer who writes code which calls the component API is licensed you can distribute the component with your application to any number of computers free of charge. Distribution to buildservers, testing or end users along with your application is free of charge.
If you change the licensed developer from time to time it's ok. You just have to make sure that in any given time there are less or equal developers working with the component than your license count.