Even the most peaceable primals, like Ramuh, can temper people just by their presence, or by a flawed summoning.

On the other hand, some primals, like Susano, are never shown to actively try to temper anyone. Alisae and Lyse are even present for his summoning, literally only ten feet away or so, and aren't tempered.

So we're left with two possibilities. Either Hydaelyn can simply choose not to temper people; or she can by her presence, whether she wants to or not, which is why she sits in the background handing out Blessings instead.