Some time around issuance, yes. But without finding past threads where datapoints on Plat status upgrade speed (for those who did not have Plat or Spire before the getting card), I would not assume any particular timing. I could possibly envision, for example, how it might possibly not be sent until your first card statement closes.

But again, I bet there's plenty of datapoints on this in some other thread from the past. But you presumably didn't look for one if you started a new thread about this now. (The 10% rebate has been available for quite a few years now, and AFAIK has worked the same the whole time.)