After reflecting on an icon it will immediately demand a tithe. Ruminate and revere are deleted. This occurs at frequent intervals in no specific order, or specific icon. They are all equally guilty.
I *think* (stressing the word think) they operate on an 'x' number of actions before requesting a Tithe. So, if you don't Tithe after each interaction it stores the actions as uses. I'm not sure if this covers your issue or if I'm correct, that is just how mine seem to react for me.
Unless you're trying to dump excess currants, I think it's best to only use the Reflect verb (for iMG), then you only need to tithe each one every fourth game day or so.