Changing IA tier to Intelligent tiering on S3 bucket doesn't apply archive for old objects

We have 2 buckets that where moved to Intelligent tiering storage class. I'll give some background and numbers for clarification and the question will be after that. I'll number the buckets 1 and 2.

1. From IA tier to Int. tiering - 80% of the objects where not accessed in the past year.
2. From Standard Storage to Int. tiering with Deep Archive - 100% of the objects where not accessed in the past year.

So from the above facts I was expecting that:

1. ~20% will go to Friquent access and ~80% will go to Infrequent Access or Archive Instant Access tiers.
2. ~100% will go directly to Deep Archive Access Tier

So a week after the change already passed and I assume all transitions are done to Intelligent tiering and the reality is that:

1. ~4% "StandardStorage", ~96% "IntelligentTieringFAStorage"
2. ~90% "IntelligentTieringFAStorag", ~10% "StandardStorage"

The names of the tiers in the last list and the percents are taken form the S3 bucket metrics.

Q1: So I assume "IntelligentTieringFAStorag" means Intelligent tiering Frequest Access storage. Am I right?
As most of this objects where not accessed for a long time, I assumed they will directly go to the cheeper tiers.
Q2: Looks like I was wrong, or do they need more time to do this?
Q3: Does the change of the tier to Int. tiering marked the objects as "accessed" and this means I have to wait 90-180 days more?
Q4: Is there a way to force the objects to go to the archive tiers, without paying again for the tier change (there are a lot of objects in this buckets).

The main reason for this change was cost optimisation, but by now, I have only increased my bill :)