When you “configure” those parameters in Live are the names exactly the same? Do you have two “configured” parameter sliders, one for each Tune and Tune depth?
If this is the case, then PULL cannot differentiate between parameters that are the same name (because it uses the name as a reference). It is not very often that this happens (there are very few VST that name their parameters the same names). We have a new program we will release soon called xPlugin which will overcome this problem. We may also update PULL to be able to handle this problem, but it will be some way off (it’s quite a complex problem to solve).
However, it could be that the “Tune depth” parameter controls the “Tune” parameter in some way. If this is the case, then it may be possible, but there may be some complex Lemur coding involved.