You seem to be confusing Vim's "tabs" with the "tabs" you can find in virtually every other program.
Unlike other implementations, Vim's tabs are not tied to a buffer. In Vim, "tabs" behave like what you would call "workspaces": they are meant to keep together one or more windows. Those windows could display any buffer and you can very well end up with the same buffer displayed in multiple windows in multiple tabs!
With that in mind, it would be very wrong to use them like you want. "Tabs" don't represent files and jumping to another "tab" is not equivalent to jumping to another file at all.
The window created by :Vex
is a normal window. Like all the other windows, it is contained in a "tab" and can't live outside of a "tab". And you can't have "tabs" inside of windows.
So, basically, what you ask is impossible.
If you are on a Mac and this "other-editor-like feature" is really important for you (more important than, say, embrace the Vim way), you could try this MacVim fork that adds a "regular" file explorer outside of the buffer/window/tab trio. You could also try PIDA which tries to build an IDE around Vim; including a separate file explorer.
autocmd VimEnter * :Vexplore
giving different netrw. – Ami