Every situation is different, so it is not possible to provide a generalization that fits all circumstances. That said, in general, I have found it better to speak of "belief systems and practices" rather than "religion" when describing the religious-like traditions of third-world or pre-industrial people. What Christianity and Islam, especially, aspired to, was very different from some of the groups you describe.

If I were raised to believe in a pantheon of powerful entities, I was usually also brought up to recognize that they were entities that were specific to my home and people. It would be hard to imagine sharing them with anyone who was unaffiliated with my group (recognizing that my group could be quite large - I might recognize that many other places had the same entities).

Outside of my group were people who had their own entities and beliefs. They seem very strange to me. I might regard them as "primitives" and as very superstitious: it is always easier to recognize other people's folklore than one's own. But generally, I would see little purpose to try to convince someone else of the validity of my beliefs - and the wrong-headedness of theirs. They have their beliefs - which suit them; and I have mine, each tailor-made for each group of people.

The "Great" religions are distinct in that they usually have written documentation, holy scripture that one can refer to, tethering the belief system and creating an opportunity for more people to subscribe to the same belief system. A "religion" is less like to change over time and place because of this - although they do in fact change. In addition, these "religions" tend to promote the concept of a higher purpose that does not normally exist in the other belief systems. Some (but not all) attempt to extend this spiritual umbrella to non-believers. Other belief systems, which recognize the existence of other deity-like entities can be vulnerable to conversion because their culture leaves the door open to other spiritual possibilities.

Most of what the first type of belief system I describe attempts to achieve is survival against dangerous supernatural elements and a safe, orderly transition through the various passages/stages of life. They may have a concept of what their own otherworld looks like, but they would be just as likely to say it is only for members of their group. The "Great" religions are typically extroverted, while pre-conversion and third-world belief systems are typically introverted.

Perhaps this will help frame your question and your understanding of the situation. As indicated, your question is very broad, and each situation describing the encounter of a proselytising religion in a third world setting is different, but these differences tend to follow the pattern described here.