When does the 90-day Non-O visa start after changing from a visa exemption in Thailand?

When you apply for an in-country Non-Immigrant visa, you will be into the under-review period, without any stamp on your passport. Your "go back to the office date" is stamped on the blue receipt. When you go back to the office on the directed day, you will get a visa and the first 90-day stamps inked into your passport, usually the issuing date (also the starting date of your first 90 days) is one or a few days before the day on the receipt.

The under-review period at CW is 15 days.

So the direct answer to your question is, no either is correct and you will know when you get the stamp.

You cannot travel outside Thailand during the under-review period. You can travel out from Thailand during the first 90 days, make sure to get a re-entry permit.