Sorry for waking up this old thread :)

I recently had the same experience with PDF::API2, and some further digging shows that it's not actually a kerning problem....well, maybe kerning is -also- not working properly, but that's not all.
The ttf-font loader seems to be broken and is ignoring the glyph width information, or something to that effect. This results in any ttf (or otf) font becoming monospaced, even though the font itself isn't.
Using fontforge to convert the font to a .pfb/.pfm pair and using $pdf->psfont to load those results in proper glyph width usage.

Maybe someone brave and knowledgeable enough on ttf internals can descend onto PDF/API2/Resource/CIDFont/TrueType/FontFile.pm and fix this.