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
.app suffix, but when launched, they actually launch a binary that's specified in
Info.plist in said package. This is the binary your alias links to, in the
Running an application from the GUI or through Launch Services (e.g. via
open) 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.
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
subl 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
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.