"Even-spoken" means calm. It literally mean speech that stays at a fairly steady pitch and rhythm. Thus, it does not indicate strong emotion. It does not mean cold or robotic, but it means calm and cool-tempered. It suggests someone who does not get upset or get angry easily.
A news announcer is usually even-spoken. "And in today's financial news stock closed slightly upward in reaction to the latest jobs report." The commercial that follows it is not even-spoken: the voice gets soft and loud, fast and slow, low-pitched and high-pitched. "Act NOW! Go to your Clunkmobile dealer for the BIG SPRING BLOWOUT EVENT! These deals won't last, so hurry hurry HURRY!"