This is correct. The game looks only at what is currently needed for kingdoms to reach their next power star.
For a pet to be possible to be offered:
- The kingdom MUST need a pet upgrade to reach its next (and ONLY next) power star (such as 13 and 17). <— This right here will stop most pets from being offered in Daily Deals.
Is the kingdom at any post-10 star level that isn’t 12 or 16? Then, it doesn’t need a pet to reach level 20 to reach the direct next power star, so no pets will be offered until the player is at the correct power star level to require a pet upgrade.
The requirement for the pet upgrade MUST not yet be completed for that power star.
There MUST be an available, non-faction, non-cosmetic pet that has been released which would fulfill that power star requirement (currently available for all kingdoms at 13, but only a few kingdoms at 17 at this point in time).
Unless a kingdom AND a the associated specific pet to that kingdom meets ALL of these requirements simultaneously, it will not be offered to players in a Daily Deal.
Note how the pet offer specifically calls out Power 13, which is a power star level that requires a pet upgrade. From the first picture, that requirement is not yet satisfied. Shortlong is a qualifying pet as it not a faction pet or a cosmetic pet. Therefore, the requirements are met for a pet offer to be issued to the player.
EDIT: Added pictures to assist in explaining the situation.