By migrating stadiums, do you mean the actual stadium and it's park factors, or do you mean the image?

If it's the actual park factors, then no, I do not believe it does, since the park factors change from season to season.

If it's the image you're talking about, then I think the issue is that you have to rename the park image to exactly what it is in DMB and then it will pick up the correct image. I seem to remember a previous thread about this, I'll see if I can use EZBoards "great" search feature to find it.

Otherwise you'll have to select the correct park image every season.