Your reviews will not show until google verifies the authenticity of the reviews given. The best way to get reviews is to place the Google Reviews badge and collect ratings and reviews from your customers on your Shopify store.
You can download Customer Review App form shopify, this app will automatically place Google Customer Reviews js code.
Please find the link here:
@dilwyn84 No the standard Shopify Reviews app is not integrated to Google so they won't show. For info regarding other comment, I added the Google review system to my site but found I got very few reviews and you can't control email reminders etc. So ended up ditching both Shopify Reviews & Google reviews and went for JudgeMe instead. I'm pretty sure it is integrated to Google (even though it doesn't show on the list you linked to, it says it is on the JudgeMe website) and I have found it very good for actually getting reviews (as it sends email chasers). I'm using the free version which meets my needs for now (I don't have the minimum of 50 reviews you need for them to show on Google yet), I think you do need to pay if you want the Google integration (but it is fairly cheap ($15 p/m) to upgrade). Worth looking at to see if it meets your needs.