Since stork spawns units from the previous shop tier, it can sometimes be difficult to remember which units it is able to spawn on any given turn. Here is a table listing the previous shop tier based on turn number.

Turn Shop Tier Previous Shop Tier 1 1 1 2 1 1 3 2 1 4 2 1 5 3 2 6 3 2 7 4 3 8 4 3 9 5 4 10 5 4 11+ 6 5

There is no tier 0, so on turns 1 and 2 stork will still spawn tier 1 units. Since the shop tier cannot go beyond 6 it is never possible for the stork to spawn a tier 6 directly, however it can spawn an eagle which will then spawn a tier 6. If you want to pill a stork in order to spawn a tier 5 unit (either just for fun or because you have a level 3 stork and you're achievement hunting!) you need to wait until at least turn 11 to do so.