I don't know if it applies to exploring but I noticed this with treasure hunting.
Since I usually have a pet looking for coins when I go to bed and rollover is in the morning for me I usually pick it up after.
I just checked the pet today to see when I would have to feed it but it was still at 100 after multiple days so while it is off treasure hunting the rollover does not affect it. [I think it did not age either]