Necro, I know, still felt like putting my two nuyen in:
I've always thought the entity in the Bottle was the free spirit calling itself Tutor, and assumed it had been freed from the Bottle after Arleesh destroyed the artifact (most likely, she was unaware the spirit would become active after being "freed" from its "prison" -- It was probably banished to a distant Metaplane and somehow managed to return into the fold (possibly losing 2 Force points in the process)).
Tutor: SRII Threats, page 92:
"Tutor "helps" the mage or shaman by linking itself to the magic-user through its special Spirit Tap power. By feeding some of its own power to the spellcaster, Tutor makes it appear that the caster can cast more powerful versions of common spells and take less drain for doing so. The spirit's payback is that the use of the Spirit Tap power exposes the mage or shaman to potential backlash that can result in the loss of magical power."
Given that the Idol acts a level 12 Power Focus (which, back in SR and SRII, raised a character's Magic Attribute (which, in turn, gave an additional number of dice to the spellcaster's Magic Pool -- dice that could be used for spellcasting or to resist Drain)), the effects of the Idol appear to be on par with the Tutor's power of Spirit Tap.
Granted, though, Tutor's Force rating is 10 and not 12. Still, the similarities are there.
Edit: Typos and amendments