I'm on a PC and I get this all the time too. VERY ANNOYING.
By the way, it's not just a Mac thing.
I thought it was just Dreamweaver trying to sync with online data.
In my case, I have a VERY LARGE folder of images of products and every time I connect to that, at random times, it will go into this "interacting with server" mode. I've tried to figure out why/when it happens so that I can anticipate and possibly avoid it happening but I had no luck finding a clue. I've been trying to figure this one out for 4 years...
My only conclusion, so far, is that it tries to sync whenever it has disconnected from the server. So, whenever it disconnects, it then has to read the entire contents of the folder and, in my case, is a VERY large image folder.
For me, it's pretty annoying because I have to process a lot of images in Photoshop and then post them to the web. When it stalls like this, my process or rythem gets messed up.
OK, good to know it's not just a Mac "thing".
I don't know if this is related at all, but my brand new Mac with 8Gb of ram was really dragging its butt, and so I phoned Mac support and they gave me instructions to do a "Option/Command/P/R" as it was starting up. I don't know if that was the issue, but it has stopped since.
I don't know what the equivalent on a PC would be for that. They told me that something was stuck in the Ram, and that this would clean it out.
If it starts happening again, I will for sure repost!
I spoke too soon! It's happening again! Good Lord!