"All Will Be One" cares about counters that are put on a permanent. the "Nine-Lives Familiar" enters the battlefield with the counters, so I don't think "All Will Be One" would trigger.
When you play out nine-lives familar, you physically put the counters in that card, all will be one sees that and says "9 countere were put on, deal 9 damage" Same reason it works with planeswalkers
Okay, so All Will Be One does care about counters. But just as you put loyalty counters on walkers (which triggers this) so too does charge counters, and so on. It does not care what the permanent is. Just as long as you are placing them. This in conjuction with Ozolith makes for some explosive turns