Just in this moment it clicked and I have understood what you meant 2 weeks ago :D
I do not know how to explain it to others but I highly recommend this: download the .gtf file from the ENSEMBL ftp server. check out the following transcript:
awk '$0 ~ /ENST00000576251/ && $3 == "CDS" {print $0}' Homo_sapiens.GRCh37.68.gtf | less
You will notice it has 4 exons. Pick exon_number "1" and enter its coordinates into UCSC genome browser hg19 like this:
chr18:2554667-2554692
Notice how I extended the interval at both sides by 1 nucleotide. Now in UCSC you will find the according transcript among others. You will see that the "intron arrows" of this exon point to the LEFT (extending the interval by 1 base makes this visible). That means (as Devon said) that the gene is on the minus strand. And now you can clearly see how it is correct that the left-most position in this CDS does NOT have frame 0. The last exon (exon 4) has frame 0.
I got it now, thanks for your reply Devon :)