It seems like there is a problem, but we couldn't reproduce the issues ourselves. Do you have custom modifications to the views?
It would be best to open a ticket so we can see your product version, maybe a link to your site where we can reproduce and further investigate this issue.
I have checked it in base nopCommerce 3.7 and Real One Page Checkout 3.7.1049.20893 with no view modification. I have documented the steps to reproduce the bug, hope this will help you to identify the problems.
1. Install realonepagecheckout.
2. In general settings of One Page Checkout enable [i]Preselect Last Customer Billing Address[\i] and [i]Preselect Last Customer Shipping Address[\i].
3. Register a customer.
4. Create two different address in the customer profile(Address #1(for billing) and Address #2(for shipping)). Try to make them significantly different so that you can test easily.
5. Purchase something and go to checkout page.
6. Preselect address will be appeared. Both addresses are same at this moment. Suppose Address #2.
7. Select Ship to same address. Select Address #1 from billing address dropdown and uncheck ship to same address.
8. In the dropdown the previous Address #2 will be shown selected but the shipping address info changes according to Address #1.(BUG 1)
9. Now select new address in the dropdown of shipping address and select Ship to same address again. And uncheck it. Address #1 information will be shown in the shipping address.
10. In this step, select Address #2 in the shipping address and again select Ship to same address and uncheck it. Now select the dropdown both addresses will represent Address #1. The data has been manipulated in the client side.(BUG 2)
Please watch the videos of my previous comment, it will help you to understand the scenario.