Tinged: Subtle body is tinged with dispositions, just like a cloth becomes tinged with perfume. The dispositions are: Virtue and vice, knowledge and ignorance, passion and dispassion, power and weakness. These dispositions are with the intelligence and since subtle body contains intelligence it gets tinged.
It is not the spirit that is migrating. It is the subtle body that is attached to the spirit remains bound, migrates. This verse 62 also confirms that nature has to perform its acts in a long sequence with its manifold creations, life after life.
Thus reincarnation is necessary to acquire experiences, for improvement of soul, to enjoy life, suffer pain, and to learn the truth that soul is not same as material world made of root material, and thus emancipate.