If the wood is wet, don't paint it. The moisture content needs to be under 14 percent which can be checked with a moisture meter. If you paint wet wood, the paint will certainly fail faster than if you painted the wood when it was dry. Painting wet wood will also invalidate the warranty on the paint. What will probably happen is the painters will see that it rained all night and will probably cancel. If they actually show up to paint wet wood then I'd say you hired the wrong guys. I don't really know that there is a 3 day rule, but it's really common sense that all painters should have. They know the sun needs to come out to speed up the drying and that if it is overcast that it will take longer to dry out. They may also show up to caulk, prep or paint areas that didn't get wet....I will do that sometimes as it may be a better option than sitting at home waiting.

For our deck exposed direct 90+ weather in fair or mild humidity dried our paint in 4 hours before a storm giving no drips or messes.

Likewise for 4 hours in more humid 90 or so degree weather, the underside of the deck dripped, especially in the last 40 minute areas we painted.

Even if they get rain, have them take out any vents you have and rinse out the meshwork inside.

Good luck.