I confirm that I have observed it enough times to say that this is most likely not a coincidence. For sure something is changed when a new supporter joins the game. Sometimes the effect is positive and sometimes it is negative, hence it has no sense because it should be either positive or neutral.
For the case of the substitution, the same thing is observed despite that it should not be like this.
Briefly, what seems more likely to happen in this game is that whenever there is change, be it in orders, formation, substitutions or the number of supporters, there is change in the flow of the game irrespective of what change has been done. This means that you may make an appropriate change and yet the outcome may to be negative. Similarly, if you make a bad change, the outcome may be positive. In other words, the game engine appears to be based on random switches rather than logic switches.