As soon as we add a new parameter using this new Multiline Text parameter type to our existing Shared Parameter file it invalidates that file for use in prior versions of Revit. If we try to access our Shared Parameter file we'll be greeted with this message.
Mulling it over for a moment, it makes sense to me since the older versions of Revit are not able to interpret this new kind of parameter because it didn't exist. Rather than allow us to continue, to create a parameter that isn't supported, it takes the hard road and prevents us from using it at all. It might be possible, via another Update Release to 2015 and for the other older supported versions, to provide code to ignore any Multiline Text values it finds when it parses a Shared Parameter file.
This means we'll need to create a separate shared parameter file for managing any Multiline Text parameters we use. We can keep on using the original Shared Parameter file(s) we already have. Just don't add any new Multiline Text parameters to it. We need to manage this new parameter type on its own, as long we expect to need to use the older versions of Revit.
Oh, if you manage to do this before finding out it won't work...you can open the Shared Parameter file in Notepad and delete the line that is dedicated to the Multiline Text parameter(s) you've created. It should work again in 2015 or older versions.
A comment (to a previous post) regarding this new feature alerted me to this issue, thanks Abe!