Page Refreshes seem to be what triggers the Random Events but donating seems to have some effect. I tried donating 5000np a day every day for a fortnight and then not. When donating I got only positive events. When not donating got a mix of positive and negative RE's.
Didn't get anything really valuable but did score more fairy quests as opposed to other event types. One thing though I did notice that many of the quests are now starting to cost more than training my pet would. So for a less than level 20 pet faerie quests are now getting more expensive than a one or two dubloon coin.