I can't provide an experience in a polyamorous situation, but when you love someone but you decide to break up because you 2 weren't going to be compatible long-term for whatever reason/s, initially you will feel really awful. You loved someone, they brought happiness to you whenever they are around, and suddenly now it's off and they are no longer with you. A friend describe heartbreak after a mutual break up as "It's like being addicted to a drug, they brought me happiness, and now without them I am having major withdrawal".

Heartache can only be dealt with through time and the body/mind adjusting to the sudden change, there are outlets to speed up the healing process of-course, but you can't expect someone to adapt to something right away especially when it has something to do with removing the feeling of love and passion they have toward another person that they care about.

I just think though that if they chose to be with you instead, then that means they care more about you, and you should really focus on that aspect by showering them with as much love and appreciation as you possibly can, reinforce their loyalty to your relationship!