I ran this program with Hands Off filtering network traffic. There was never an attempt to contact any Google server, though it did contact Amazon's S3 network when I asked it to check for updates.
I'm usually a cheapskate, and I've been very happy with Screen Sharing - the built-in remote desktop software from Apple. However, I got this with a bundle, and I have to say, "Wow!"
Jump Desktop is extremely fast. I have been using it to connect to other Macs of varying OS levels on my home network and it's considerably faster than making the same connections using Screen Sharing. Screen updates, cursor movement, transparent clipboard transfer, all works very nicely indeed. My network is Yosemite and Lion, for the most part, and I haven't had any issues at all. Even my old Tiger machine is able to participate. I'm not sure if I would pay full price for this, but if you can get it at a discount and you need remote screen sharing (at least on a local network) you owe it to yourself to try out Jump Desktop.