Казалось, последствия стали ей понятны и вызвали приветливую улыбку.

В примерах с первой страницы результатов поиска по запросу "welcomingly" слово во всех случаях можно перевести как "приветливо".

They are protective of me in my old age,” he said, approaching Jason with his hand stretched out welcomingly. (Jorge Juarez-Bagdigian, "Hunter's Vendetta")

I press it, it lights up welcomingly. I give life to 31, top floor. I can feel it ascend, to Lucretia, to sister moon, into the heavens. (Hallow Harvest, "Halloween Machine Issue Four")

She seems to understand the implication and smiles welcomingly. (Lyda Morehouse, "Fallen Host")