The product ratings will begin appearing on Shopping Campaign ads whenever your business and the product itself qualifies for the program. Google is a bit vague exactly how to qualify...The rule is to gather a minimum of 50 reviews across the store before submitting the form to apply to participate in the program, but that is where the hard & fast rules end. In this article they say, "Reviews and star ratings may not always show. We’ll show star ratings when our system determines that the information is accurate and relevant for shoppers’ needs." Which means they are leaving it up to an algorithm and the parameters are left a mystery.
The only way to get reviews that aren't made directly in Google to appear in the ads is with a reviews aggregator app. Here's an article explaining this and offering a few alternatives. And here's Google's comprehensive list of approved 3rd party aggregator apps.
There is a section of your Google Ads account where the seller rating stats will begin to populate once the ads are showing the stars. The only way to know whether the ratings are showing is to occasionally check recent dates in this section. Here is how to get to it: Click on "ads & extensions" and then "extensions" and then scroll to the bottom of the screen and choose "automated extensions." The "Seller Ratings" row will populate with data on days when the ratings appeared in the ads.
If you aren't receiving enough reviews to qualify for the program or to keep the stars actively appearing on your ads, here is a tip: Use your review app to create an automated email series that asks customers to review. Schedule a large amount of emails and be very direct about wanting a review. Make sure to set up a trigger inside his review platform to stop the emails as soon as the person leaves a review. The automated emails have to be sent out of his review platform to do this, of course. He said he sends emails that say things like: reviews are so important, we're a family owned business, your voice matters, if you can’t give us a 4 or 5 start review please let us know so we can make it better, and even "we’re not going to stop asking until you review." Sounds pushy, but effective!