During a replay of a dry lap with soft tires, replay begins to my surprise with rain tires, that later change to soft tires. Was with F1RFT2013 mod. Race and replay done with build 982, in the same session from the race menu. Cheers. P.S. Later I restarted RF2, and from the menu option, then replay, the rain tyres didn't show.
Bear in mind the hotlap replays are like a cut out of the 'normal' full replay, and stuff like tyre compound isn't automatically inserted at the beginning point (in a full replay all cars start in the garage, and when they actually jump 'into the car' the tyre compound info is set; so you never see an incorrect compound when playing forwards from the beginning). When starting a hotlap replay, or indeed stepping to another timepoint in any replay, the tyre compound may take a little while to update. As long as it's not possible to change compound while on the track it's safe to assume the changed-to compound has been on the car from the start.