If you look at this pic of my Birdy you can see the chain is also on the biggest cog on the back but that the derailer is a fair bit higher. This is due to a shorter chain. With the Birdy there are some things which are critical to the success of the rear derailer function: Chain as short as possible, derailer must have a long cage, or the chain won't be gathered adequately when folding.

The shifting problems sound like the cable adjustment must be increased, ie screw the barrel adjuster so the cable housing gets longer.