Hiya, while Im not 100% sure, it looks like the timers do run on timers alone.
According to the docs:
Chat Lines - This is the minimum amount of chat lines (measured in lines per 5 minutes) required to activate the timer. This is useful in slow chats to prevent Nightbot from spamming in an empty channel.
I would try setting the chatlines to 0, and measure if the interval times are correct.