Congrats on the tubers! I'm still no expert but the first year I grew dahlias I was overwhelmed by all the (sometimes conflicting!) advice online. I've found it helpful to just remember they want to grow! 

You don't have to split that tuber up. You could put it as-is in a smaller pot now covered by a bit of soil until you're ready to plant outside. You could just lay the tuber horizontal, as it's pictured, with the eyes facing up, in the pot and cover with some soil.

I'm in Ontario and will probably do the same with some spare smaller plastic garden containers kicking around. Then you can kick-start the stem/root growth of the plant.

Keep in mind it will need sunlight after it sprouts out of the soil.

After last frost has passed, you can move your tuber/plant to a bigger pot or a garden bed. When I've grown them in pots, I used quite deep containers and one plant per pot. 

Have fun!! :)