Joe is correct on everything. I seem to get a lot of pods on Tiger Babies even if I don't pollinate it at all . These are usually chaff. I believe Tiger Babies are triploid and most if not all of your Asiatic lilies will be either diploid or tetraploid. Try to match diploid with diploid and tetraploid with tetraploid.
Use the lilium data base here to find the chromosome count of your hybrid lilies. For example, Yellow Whoppers:
Lily (Lilium 'Yellow Whoppers') you can see is tetraploid. I have entered the ploidies that I know in the data base. If it is not entered then assume it is diploid. We don't always know what the ploidy is, especially the Dutch introductions.
Use pollen from lilies having the same ploidy as your intended pod parent. For example, this year I used pollen from Pearl Melanie on Yellow Whoppers and vise versa and I have pods on both. Here is Pearl Melanie showing that it is also tetraploid:
Lily (Lilium 'Pearl Melanie')
Link to lily seed starting:
http://www.pacificbulbsociety....
Most common garden lilies on the market are either immediate epigeal (Asiatic, trumpet, orienpets) or delayed hypogeal (Orientals, martagons).
Finally, here is a link to the germination methods for species lilies.
http://www.pacificbulbsociety....
If you have any questions about a particular potential cross just ask here first (next lily year).
