Pasting text on Vim inside tmux breaks indentation

Question

My .tmux.conf file was initially empty, but then I edited by basically copying the Linux part of this answer from UnixSE. The problem below occurred both before and after I edited that conf file.
I tried to copy text from a website. When I'm using Vim in bash without tmux, I can paste the text to Vim without problems and it looks like this:

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. 

Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. 

Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. 

However, when I'm inside tmux, the indentation 'breaks' and I get something like this:

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. 

  Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. 

    Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. 

That has never happened when I paste the text on Vim inside bash (without tmux). And, in case it matters, the way I usually copy and paste is by selecting the text on my web browser, then pressing Ctrl+C , then going to Vim, enter Insert Mode, and finally press Ctrl+Shift+V .

How can I make Vim inside tmux paste my text the way it is in the block in the top?
What do I need to fix?

Answer 1

So using :set paste first can resolv the issue.

as you asked here is my tmuxrc but it is very short :

:~$ cat ~/.tmuxrc
set -g status-utf8 on
:~$

So I don't think it is special

Answer 2

Manually toggling :set paste/:set nopaste as suggested by francois P is cumbersome, and resetting the TERM variable as evaristegd suggests is a very bad idea as explained in the comments (which hint at the better solution below). The best solutions that I could find are explained here, and I'll briefly repeat them below.

Background

The central concept for this problem is "bracketed paste mode", which lets a program distinguish between pasted and typed input. The problem is that vim 8 only enables bracketed paste mode when started with certain values for the TERM-variable (e.g. TERM=xterm-256color). Within tmux however, vim should get either TERM=screen (default) or TERM=tmux, and in neither case does vim enable bracketed paste mode (I have no idea why not, please edit if you do).

Solution

Add the following to your ~/.vimrc, as explained in the vim help: :h xterm-bracketed-paste.

if &term =~ "screen"                                                   
    let &t_BE = "\e[?2004h"                                              
    let &t_BD = "\e[?2004l"                                              
    exec "set t_PS=\e[200~"                                              
    exec "set t_PE=\e[201~"                                              
endif

Answer 3

Edit: As pointed out by others, the original answer is wrong, and I plan to delete it later, if the admins don't oppose to it. For a good answer, please check DiningPhilosopher's one.
If you want to see the original answer, you can check the edit history.