How do visualisation meditation practices relate to insight? A while ago I attended a Tibetan Buddhist group. They were very nice but I just couldn't get on with the visualisation practices. I find it reasonably clear how mindfulness of breathing becomes an insight practice and metta bhavana. But I just couldn't see how an intricate visualisation practice would lead to an understanding of conditioned existence, suffering, no fixed self or any of it really. How do visualisation practices relate to insight?

Additional detail - the practice involved the Buddha in a bright blue sky on a throne and I remember there were snow leopards under the throne and light was going out of the Buddha.
1)
Ultimately, the "core" of Tibetan Buddhism is the Mahamudra system of practises, where they also include the Samatha and Vipassana systems/methods as described in the Theravada texts.

The practise of visualizing "Buddha on a levitating throne flanked by snow lions" (paraphrase) is an overly-promoted for-absolute-beginner entry practise mainly because it could be taught under 15 minutes. Having said that - under the guidance of a qualified teacher, it can lead to results similar to those of the kasina practises.

For a variety of psychological reasons, most individuals find it more exciting to visualize some made-up super-beings instead of pieces of earth or colour discs. 

2)
The Visudhimagga prescribed and recommended different Samatha meditation objects depending on the individual's intellectual and habitual dispositions. While anapanasati works for most people, kasina works for the others. In a meditation retreat, the teacher may not prescribe the same practise for everyone.

3)
Samatha meditation practises is not unique to Buddhism, and they have been around even before the historical Buddha. The main difference is that the Theravadin's Samatha practises are stripped of all mysticism (incantations/rituals/super-entities) - leaving only what truly matters.

4)
Vipasana is what sets Buddhism aparts. It is vipasana that leads to genuine insights and liberation from dukha. The Theravada texts tell of bikkhus who obtained final liberation just on vipasana practise alone, but the same texts strongly recommended the cultivation of Samatha skills to support and to "supercharge" the practitioner's vipasana experience.