Ok, I have to get faster at these "i dont think it works that way things".
You don't get +1 Magic or Resonance on initiation. This effects you Laughing Mage.
You do get +1 max rating, but no actual bonus on the spot. You then have to also raise the rating later.
So for mages:
1) your max magic is 6 (-essence loss) + Initiation
2) Initiation gives metaplane access the first time
3) You gain a metamagic
So, for 13 Karma you get effectively a metamagic, in the case of LM it may still be worth it - centering is like adding 1 to logic or willpower for drain purposes - so taking your willpower from 4 to 5 would cost 25 - initiation costs half this and gives a bonus vs drain.
Samantha has been taken as a contact so I had a look at her, she is built totally wrong too, her essence loss is six - making resonance 0 - submersion is limited to current resonance (as magic and initiation are linked). Therefore she needs a re-build seeing as two characters have her as a contact now.
Both errors, the +1 magic per grade and the non-matching ratings, are third edition rules.