Can I report my 90 days from Rayong after moving from Pattaya, or do I need to report it in Pattaya first?

You do your 90 day report the end of August (from 15 days early to up to 7 days late) wherever you are living at the time.

We moved from Bangkok to Rayong last year. There was no requirement for a TM28, just the TM30

That is totally up to you, move and submit TM 30 at Rayong and 90 days report there at once, or complete reporting 90 days in Pattaya in advance, then move to Rayong and do TM30. Either would work.

You need to go to the Rayong office to be sure TM30 is enough for proper moving into the province, or if you need to submit TM28 or anything else.

Personally, I would go to Rayong to do all at once: submit TM30, check whether TM28 is required or not, submit the first 90 days report there in person, check if the next 90 days report can be done online, etc, but it may be only me.