Li Yi was able to summon Alleria not because he took her as his pet, instead, he had simply spent some money to hire her.
The Defiants' Confederation was an interesting group. Many were eager to increase their reputation with this faction in his past life due to the fact that it offered mercenaries. Anyone with good standing could spend money and hire them to assist in battle.
A player could hire mercenaries while tackling a dungeon, battling a boss in the wild, farming minions, or any such activities with similar nature. However, in a player-versus-player situation, the mercenaries would not intervene. Their role was confined to player-versus-environment situations.
One could only hire them if one's affinity with them had reached Worship. Li Yi had achieved the latter with Alleria but not with other members. As such, the only member he could summon at the moment was her.