I would also like to know the answer to this question
I've had a similiar question when I was making a maze game with auto-generated mazes. I simply assumed that the sequence would be the same for all clients, and it does work for the large majority of the players. However, I began to doubt that assumption when I saw 2 players running through walls in the maze, it turned out they saw a different maze on their screen. They were using 1.0.2 (I forgot to ask about the OS), while everyone else was using 1.0.4
It might have been a very rare bug in my maze resource, but I couldn't find any mistakes in my code so, to be safe, I dropped the lua random function and went for a custom lineair congruential generator.