What happens if I subscribe Cursor pro and register (OpenAI) API key simultaneously?

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May I ask if we misunderstand each other?

I meant I expect something like this.
For instance,

  1. On Monday morning, I subscribed to Cursor Pro.
  2. I also registered my OpenAI API key in Cursor.
  3. On Monday, I made 9 requests to o1-mini from Cursor.
  4. Since Cursor Pro provides 10 requests per day for o1-mini, I was not charged by OpenAI.
  5. The next day, I made 11 requests to o1-mini from Cursor.
  6. The first 10 requests on Tuesday were covered by my Cursor Pro subscription, but the additional 1 request was executed using the API. Thus, OpenAI only charged me for that 1 request.

Conclusion(Expectation): API cost is $0 on Monday, but not on Tuesday.

This was my expectation and I wanted to know whether this assumption is true.
Do you mind if I ask again, to make it sure?