Yea you have to wait for the right moment to start providing them the funds. I've begun to get the timing down pretty well since it seems the AI factions go through cycles of activity. First they build up their infrastructure, then they build up their military, then they conquer, then they consolidate. Not all factions start on step 1, such as the Brutii who tend to start off by immediately heading into the greek peninsula. As soon as you see them getting their armies together, send over some money. The sudden influx means that they can extend the army build up time, which in turn forces them to conquer more, which results in them gaining a far greater income and troop production areas. However should they get the money during the infrastructure or their consolidation phase, they will instead take more time to develop their cities with the money rather than their armies. So while they would be able to eventually launch their assault, it will take a while longer before it occurs.