technically speaking you can change your active dimstyle before placing your dimensions and the dimensions will be created in the active style. Or you can select your dimensions afterwards and change their style in the properties palette.
Changing from MS to PS will not cause AutoCAD to change the dimension style automatically. You still need to do it manually or have an active lisp with a reactor that tracks changes between MS and PS and changes the style for you.
But why do you need to differentiate between PS and MS in your dimensions? You either place all your dimensions in Model Space or you place them all in paperspace. Most of the time model space dimensions are used for 2D drawings. You can make them annotative if you need to show them in different scales without affecting the legibility. Paper Space dimensions are something I have always tried to avoid, but I do use them to dimension different views of 3D parts. I find it more clean than creating them in the model space.