The cooldown period varies by spell, which may not be accounted for when the preview clip loops. The delay on some is only a second, while others may be 5 seconds or a minute, etc (should be listed in the description).
I think you are suppose to be able to have more than one summon with that skill, but it may have been broken, at least before the patch. I'm not sure if summon mastery was fixed, but you could save before trying it, if nobody who has used summons responds.