Part of the culture is that the marriages are still based on love, there just isn't the societal pressure to make that last FOREVER. Like the one woman said - she finds it incredibly offensive when outsider men come in and assume she will sleep with them just because her culture allows a woman sexual freedom.
The fact that a woman can have multiple relationships with multiple men is only mentioned once (maybe twice?) that I remember, so my guess is that everyone knows who the fathers are in most cases. One man even said if he ever has a child, he would like to buy him/her clothes once in a while even though the main male support would come from uncles.