I placed my mana collector near a terra-steel setup and tried to bind my flowers to it but it seems the mana doesn't go into the spark network at all.

Have you tried placing a spark and a recessive augment on it? That worked for me.

Yep the spark is missing. It's essentially a little mana storage that can directly be accessed by flowers and sparks.

I then suggest you to change the description as it suggest that it works without anything else.
Putting a spark alone won't work.
A schema would also be nice