What happens when you background a function which calls another function?

Question

Question says it all on the tin. Can someone explain to me what goes on here ? I'm trying to find out how to background a process in a script that calls another function and reliably terminate it when ready. Wondering whether I will have to move it all into one function ?

function dosomething {
    while :
    do
    printsomething "doing something"
    done
}

function printsomething {
    echo $@
}

function otherfunction {
    dosomething &
    TMP_PID=$!
}

function killsomething {
    quit_test=`ps -p "$TMP_PID" | sed '1d' | awk '{print $1}'`
    if [ "$quit_test" != "" ] ; then
        (kill $TMP_PID >/dev/null)
    fi
}

## MAIN

    TMP_PID=""
    echo "starting program"
    otherfunction
    sleep 5s
    killsomething