They occur each week at the same time. One started a couple hours ago. On the world map if you hover over the tournament icon when it is greyed out it will show you a timer until the next tournament and which relic it will be.
Another way to tell the relic is when looking at the boosts in your main hall they are shown in a specific order, tournaments follow that order from left to right. So this tournament is marble which happens to be the first one in the cycle, the next will be steel, then planks, etc. Below is a graphic to illustrate this (copied from a different but similar discussion)
The numbers in the graphic relate to the catering costs