Dreamweaver git files and put files

Question

I'm a little confused on how dreamweaver works in relation to my local server, testing server, remote server and my git repro.

This is for my work and I'm still learning, i'm a newb, so please be nice. I'm looking for best practices when it comes to workflow on dreamweaver.

Current workflow (and context to my question):

• I work off of my individual branch from my local server.
• When I'm done editing a file, I test it out on my testing server to see if it renders right.
• If it's good, I stage and commit it.
• I then merge my branch with the master on GitHub
• Then I go to my git panel and fetch all the changes from my repro to my local master branch to make sure everything in my local is even.
• I then pull origin master to production (remote), where everything is live and working great.

So what happens if a coworker deletes unneeded files (deprecated files) and merges his changes on the master branch? How do I make it so that my testing server and remote server are completely in sync with my local master branch? Everywhere online said to use the Synchronize with Remote Server panel and select the "Put newer files to remote" option with "Delete remote files to remote", but after some testing on my personal files it doesn't work right.

I was in the understanding that if my local server is updated with the master branch, I could just go from local to testing and at the top of my testing server click the "Get File(s)" down button. This way both servers are in sync. Meaning those deleted files from my local server will also be deleted from my testing server, right? And the same goes with the remote and local server? But unfortunately my coworker says that's not how dreamweaver works. That the "Get File(s)" and "Put File(s)" button does the same thing and won't delete files from testing.

How do I sync and match all my servers (local, testing, and remote) without using the Synchronize with Remote Server panel? And since there are too many files I cannot manually check and pull them. Please help.