What is not in the gameplay mechanism article, but has already been confirmed by @yabapmatt, is...

You got me scared for a minute that I forgot to include that! But I just want to clarify that it was included in the "Teams" section:

Summoners can only summon Monsters that hail from the same Splinter as them, so that means that all of the cards on a Team must be a part of the same Splinter, with the exception of Dragon/Purple summoners (more on that in a minute). For example, if you choose Malric Inferno as the Summoner for your team, then he can only summon Monsters from the Fire/Red Splinter.

In any case, you're absolutely right that summoners are a very important part of the game and probably the most important card to level up. Let the fun begin!