My car (2003 CVT) has a minor problem with the transmission slipping...fortunately it's not as bad as I've read with other people so I ignore it. And--it does go away or get better if you change the transmission fluid, which I do regularly.
It doesn't feel anything like the tires slipping, it feels almost like a small lurch (in my case barely perceptible)...so I would suspect that you may be actually dealing with a tire problem and not the transmission.
In terms of the tires, there is often a tradeoff between low-rolling resistance in tires (which leads to better mileage) and ones that have better traction. But the Dunlop SP20FE, from what I found online, is a run-of-the-mill tire, not specially made for low rolling resistance. On the other hand, a survey I found on a website
(sample size of 60) shows only okay (not great) performance under wet and winter conditions. Also reading the comments there, one of the posters said they had problems with these tires slipping when they were new-ish, after putting them on a 2005 HCH. So...it could be that this just isn't the best tire for traction in wet conditions.
Also...how inflated are your tires? I've read about a lot of people on this board hyperinflating the tires, which I think is a bad idea because it greatly reduces traction. Hyperinflating tires reduces the contact between road and tire, which reduces both traction and friction--the two go together in a sense. If your tires are too inflated I'd let some air out.