What actually causes the map to change?

Aha! I found it!

There are two ways to trigger a Clash, according to the game's website.

• Five (5) total rampages have been triggered between the Guardians. Whether one team gets all five or both teams have a cumulative total of five (regardless of whether either scores a Wound), the game progresses to the Clash.
• When either Guardian has only one Wound left. Even if it only takes two rampages, the game will immediately proceed to the Clash if a team manages to score two Wounds on the enemy Guardian.

Additionally, there is a progress bar visible on the HUD that indicates how near you are to a Clash.

Each diamond represents a rampage: green indicates a rampage for your Guardian, and red represents an enemy rampage. Watch your HUD for the transition to the Clash and follow your Guardians to the new Clash location.