The rules seems to conflict a bit in circle casting. The first bit says this:

Secondary Casters

Casting a Circle spell requires that one or more other spellcasters, called secondary casters, lend their magic to the spell. A secondary caster must have either the Spellcasting or Pact Magic feature to participate in a Circle spell.

After you initiate the spell, each secondary caster takes the Magic action to contribute to the spell. A secondary caster can take this action only while within 30 feet of you and before the start of your next turn.

But when you get to the options you want to use some of them say you don't need an action from the secondary caster.  For example:

Prolong

When you cast a spell that has a duration of 1 minute or longer, you can increase the duration of the spell depending on the number of secondary casters contributing to the spell, as detailed in the table below.

Each secondary caster contributing to the spell must expend a spell slot (no action required). If the spell fails, these spell slots aren’t expended.

Other options, such as Augment, do not have the text about "no action required".

Augment

When you cast a spell with a range of at least 5 feet, you can increase the range of the spell by 1,000 feet per secondary caster contributing to the spell, up to a maximum of a 1-mile increase

What does this mean for the secondary caster?  If I (the caster) cast Spirit Guardians using the Prolong option and I add 1 secondary caster, does that mean my spell fires off after the secondary caster's turn BUT during the secondary casters turn they can still perform some kind of action?  It's very confusing.  I've never seen example game play of this.

It means that expending the spell slot doesn't require an additional action beyond the Magic action they're already taking to contribute to the circle casting.

You're not alone on this, SirBarnick. Another poster here had the same doubt: New Circle Casting Mechanics (wagnarokkr also clarified the rules there)

Thanks for finding that!