The reason it doesn't work is that you have the wrong alias. Here's the correct one for Sublime Text 3:
alias subl='/Applications/Sublime\ Text.app/Contents/SharedSupport/bin/subl'
This is an alias that Sublime Text specifically provides for macOS. It will not block execution and—by default—open files in a tab next to the ones that are already open.
If you want to know more about why your alias didn't work, read on.
Application packages in OS X have an suffix, but when launched, they actually launch a binary that's specified in .app in said package. This is the binary your alias links to, in the Info.plist folder. MacOS
Running an application from the GUI or through Launch Services (e.g. via or osascript) makes OS X open that binary, but at the same time ensure it's only launching one instance of that app. When you call the binary directly, you bypass this restriction and launch another instance of the application—unless the application has measures for preventing two instances from being launched, which normally OS X handles. open
Also, as a side effect, launching the binary will block the terminal execution until you exit the program or suspend it to the background. Using the built-in from Sublime Text returns control to your terminal, as it actually uses a Launch Services call to open the Sublime package instead of addressing the binary in subl only.MacOS
Since you're basically launching a second Sublime Text instance, it'll show you the files it previously had opened, because that's its default behavior.
It is possible like this:
open_files_in_new_window setting) 

There's a macOS-only setting which does exactly that (taken from ):Preferences.sublime-settings
// OS X only: When files are opened from finder, or by dragging onto the
// dock icon, this controls if a new window is created or not.
"open_files_in_new_window": true
When using the command-line, you can use the switch to append to an existing window:-a
subl -a index.html
The same switch could be used on Windows by modifying the default open action in the registry.
Go to Preferences -> Settings-User and add there: "update_check": false
EDIT :
If it's not working then add this line in your host file127.0.0.1 www.sublimetext.com
File Location
Windows : c:/windows/system32/drivers/etc/hosts
Linux : /etc/hosts