Usage Tier Not Upgrading From Free Tier

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This language is more helpful than the documentation, and should address your concern:

Facing Rate Limit Issues with o4-mini-deep-research Model

Yes, the language is wrong in the platform site and must be fixed. A version without mistruth: Your tier level is recalculated at the time of making a new credit balance purchase, based on these criteria: the time between the organization’s initial credit purchase and now, the cumulative amount then paid to OpenAI to purchase API credits. You must interact with the payment system to receive any tier re-evaluation by making a new credit purchase; it is never automatic.

The time since that first payment must be over a week, a waiting period to detect initial fraudulent use.