I've PowerlineSymbols.otf font installed, but can not figure out how the ~/.tmux.conf.local copy uses the right code points for tmux_conf_theme_left_separator_XXX values.
If you followed installation instructions, you did
$ cp ~/.tmux/.tmux.conf.local ~/.tmux.conf.local
Now open your ~/.tmux.conf.local copy and uncomment lines 131-134 like this:
tmux_conf_theme_left_separator_main='' # /!\ you don't need to install Powerline
tmux_conf_theme_left_separator_sub='' # you only need fonts patched with
tmux_conf_theme_right_separator_main='' # Powerline symbols or the standalone
tmux_conf_theme_right_separator_sub='' # PowerlineSymbols.otf font
Then hit <prefix> + r to reload the configuration.
After uncommenting lines 131-134, this is what I get.
Screenshot of the installed fonts.

Screenshot of the tmux.

OS: Ubuntu 16.04 LTS, 64-bit
Likely you installed a font with the old Powerline codepoints
Is the documentation at Install Powerline Font the right and way to install the latest of Powerline Font?
I would assume it's the case.
You need to make sure you didn't mess the encoding of your ~/.tmux.conf.local which should be encoded in UTF-8. I also believe that your OS locale should be UTF-8 compatible.
You need to verify whether the font you installed contains glyphs for U+E0B0, U+E0B1, U+E0B2, U+E0B3 code points.
Make also sure you meet terminal emulator requirements.
E.g. rxvt-unicode must be compiled with --enable-unicode3.
Hope that helps.
OS locale is UTF-8 compatible.

Font I installed contains glyphs for U+E0B0, U+E0B1, U+E0B2, U+E0B3 code points.

Well, as per your screenshot, in the font you installed glyphs rendered for U+E0B0, U+E0B1, U+E0B2, U+E0B3 code points are not the powerline symbols:

I don't really understand what's wrong. This is what I have in ~/.tmux.conf.local file.

As per your screenshot, they aren't the same.
What's wrong is your font setup.
You have 3 options:
PowerlineSymbols.otf font and double check your terminal setup supports fontconfig, as instructed in the matrix in the Powerline manualtmux_conf_theme_xxx_separator variablesThis is really external to my tmux configuration 😐
@gagan0723 check out this gist that shows you how to install Powerline fonts.
Most helpful comment
If you followed installation instructions, you did
Now open your
~/.tmux.conf.localcopy and uncomment lines131-134like this:Then hit
<prefix> + rto reload the configuration.