How do I know if a filling I make needs to be refrigerated? Is it those with just eggs or milk? What about heavy cream?

If it has eggs or cream cheese in it I would definately put it in the fridge. Also if it's one of those that'll turn into a puddle if left out (like whipped cream or mouse) I'd put it in the fridge also. Anything else I'd say can be left out.

Generally, if the major ingredients are perishable, it would be best refrigerated. Something like ganache, with is about 1/2 cream is considered "safe" on the counter for a day or two, but in hot weather it will melt. Better to be safe than to make someone sick.