The oil dipstick is VERY long (as you know), and it takes a while for the engine oil to warm (by convection) the entire length of the dipstick. Also, the top of the dipstick where it seats in the tube doesn't have a positive seal - which allows air to enter.
As the engine (and oil) warm up, the air around and inside the top of the dipstick tube is gradually warmed... faster than the dipstick at it's top near the seat. Moisture from the warming air in the top of the tube will condense on the cooler top portion of the dipstick (picture a cold beer on a hot humid day). The iron particles in the steel dipstick rust from the moisture. As the entire dipstick warms, the moisture will evaporate - exposing the rust.
If that process worries you, pull the dipstick out frequently and coat the top portion with oil, which will prevent oxygen/moisture from contacting it. Otherwise, sleep well. There is no reason to panic - it won't damage your engine unless a significant amount of rust/debris falls down the dipstick tube. But hopefully you are checking your oil/pulling the dipstick frequently enough to prevent that.