You are making a common mistake for random numbers.
See the MSDN Documentation on
Random[
^] Seeding.
Random numbers are actually pseudo random and the clock is used by default for its seed (you can provide your own though).
To solve, you can make a single random object and have your own seed value (int) rather than the default.
Random _randSeed = new Random(GetSavedSeedValue());
...
if (seconds % 5 == 0 && seconds != 0 && animal_appearance == false)
{
animal_appearance = true;
Last_animal += seconds;
anime_Index = _randSeed.Next(9);
}