Background script run at login interrupted when I run tmux in terminal

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http://unix.stackexchange.com – In ~/.profile I run a script in the background (redshift for changing the screen temperature at night time). After logging in, I can open a terminal, and run tmux. However, at this point, redshift visibly get interrupted as the screen temperature resets and it seems that redshift starts again in this terminal. What's happening here? I get the impression that ~/.profile is for each shell, and gets parsed again when I run tmux. Could this be? (HowTos)