Today I logged in to my laptop at home from work which was already running a tmux session, so thought yea just attach cool can continue with what I was looking at at home. I forgot that the keys would be the same ofcourse, and was unable to use the tmux session at my laptop at home. Whenever I would type Ctrl + B + n etc it would do that on my work desktop which was also running tmux. I was lolling oh damn how to get out of that laptops tmux session.
Google to the rescue. Here is the solution:
If you want to access the tmux session inside the ssh session so in my example on my laptop, you have to just use Ctrl + b + Ctrl + b
So if you want to detach the nested tmux session you have to execute the following: (Ctrl + b) + (Ctrl + b) + d.
(Resource: Tmux Tips)