Printed page 103 gives intransitivity and responsive action related to Faʿlala for this pattern.
طَمْأَنَهُ فَاطْمَأَنَّ
Translation: He reassured him, and he became reassured.
Earlier actionResult
Making someone feel settledBecoming settled or reassured
Causing a stateReceiving that state
The example illustrates a semantic relation between two verbs, not merely the presence of extra letters in the resulting form.