It seems like the soil would be warmer at the horizontal level for faster root and shoot growth, for one thing. That's my guess, but I've planted plenty of tubers at an angle to accommodate a funny-angled stalk as well. I don't think it matters that much in the long run.

Ditto to what Pooch says.
Usually I plant horizontally, but sometimes it was necessary to plant them a bit more vertically. Didn't seem to matter to them.

I planted my first dahlia tuber with the eye pointing down. Poor soul found its way up after many days. We had a good laugh considering what a fool I was.

That said, I planted all my dahlias in 16"x14" square planters. They are already staked.

Here is a link that might be useful: ADS Growing Dahlia in Pots

You can plant them either way but some are really long so you don't have to dig as deep a hole if you plant them laying on their side. We have a friend who uses a large auger & electric drill to dig her holes straight down, pops in the tuber & covers it up. She gets kidded that her dahlias are going to get tired standing up all summer- but they grow well & don't look tired to me!