People can only see a summary of what all their connections have said about them. They won’t see the details of who said what about them. And they will only see the summary of data if they accept your connection.
They will see a preview of why you value them in their homepage – but this is the only place they will be able to link what you have said back to you.
Their dashboard works in the same way as yours does. Just check your My value dashboard including the What others said tab to get a better understanding of how much detail they will see of your answers.
You will notice that the tags you can attribute to your connections stay private and will only be visible to yourself.
Depending on the project you are in, the message of appreciation that you write at the end of the adding a connection may be shared with your connection throughout the process. It is currently not part of your dashboard.