So you have:
blu/vio = hot
gry/brn = neutral
The blu & vio have dots, so the dots on the secondaries are hot (they also need to be connected together, and un-dotted two secondaries together--neutral). So the two dotted secondaries (likely 115V in your explanation but can't be sure based on your explanation) are hot and the other two are neutral.
OK, I just took a look at the softstart pdf....it actually has the diagram for dual primaries like you have. Blu in the PDF is neutral and Black/Brn is Hot. It is confusing because it shows 0V/-115V, which should be 115V/0V respectively for non-inverting polarity transformers like we have. In that diagram, I read 0V as Hot and -115V as Neutral, I could be wrong but it doesn't make sense otherwise.
According to that PDF (which I skimmed, not read thoroughly!) it looks like you connect the softstart before the transformer, not after. This is usually the case for softstarts but I haven't tried this particular one. Ask Kevin H of DIY Cable, as he has praticle experience with this one, or when I get more time I'll read the PDF and make for certain.