The soul starts its journey from darkness and in its early births it is not inclined towards the Divine. It is rather asleep and the person goes through quite contrary experiences including denial or even hostility against the Divine.
As it develops, then slowly it is drawn towards the Light with or without devotion, through a Divine Name and Form or through the formless. If it is a progression of Avatars, then it is likely to get drawn to Sri Rama when it is more sattwically inclined, and later to Sri Krishna in the same or another life when it seeks to go beyond sattwa.
The journey is through lives and what happens in one life cannot be taken as the soul’s final resting point.
The steps and stages of evolution are fixed. However one cannot say that if a person is a devotee of Lord Rama in one life he will stop evolving and rest permanently in the world of Lord Rama. Besides what do we mean by a devotee? It is very rare to have true bhakti. Transactions and rituals are not bhakti. Besides most souls seek perfection and are unlikely to be satisfied with staying forever in any intermediary world. The soul has come from the Supreme and cannot rest until it finds rest in the Supreme. Resting in the world of Lord Rama and Sri Krishna is not the end point of the soul’s evolution but a temporary Resting place.