Should this be happening?

You are running the msi. click this to get the actual launcher.

https://launcher.mojang.com/download/Minecraft.exe

I don't know much about the new launcher but I don't think it should be happening. With the new minecraft launcher, it should install the minecraft shortcut on the taskbar. Are you opening the launcher you downloaded by mistake?

If you notice that it says "Launcher" - It doesn't matter when it pops up, but Minecraft finds a lot of Data from the Internet (Connections to servers).
Also if you cut off the Internet to your PC and try to start Minecraft, Log out, You'll notice you can't log in again.

That's because the "Launcher" you're worried about is your friend here. It goes on the Internet and finds the stuff you need to launch Minecraft for you