CHANGES OVER TIME
The souls attracted by the Circle's enchantments are the souls of those slain in the wilderness – such as those slain in battle. Therefore, more battles on the tournament squares means more souls available.
Each week, the 10 bloodiest squares – the tournament squares where the most units have been slain – start to attract more souls each hour. (This is number of troops slain, not XP value. Diplomats, gatherers, wild animals do not count.)
The 10th bloodiest in the preceding week attracts an extra 1 per hour, the 9th bloodiest attracts an extra 2, the 8th bloodiest an extra 3... up to the most bloody, which will attract an extra 10 souls per hour.
These changes are cumulative, week on week, and persist for the duration of the tournament. So, throughout the tournament, the most fiercely contested squares will become more valuable. (The most extreme possibility would be that a single square could be the bloodiest every single week. After 4 weeks it would be gathering an extra 4 * 10 = 40 souls per hour, 50/hour in total.)
If I understand this correctly, then the most that any square should be able to generate is 30 souls/hour for the third week of the tourney. Some squares are now generating over 30 (up to 40) souls/hour. Is there a bug in how the modifiers are applied?
Of course, I could simply be mistaken (as is most often the case).