There is a timing issue anytime the players disagree on timing. This only matters when something affecting one player will have an impact on another player as well, but really anytime the two players wish to know "what happens first" between their independent decisions, initiative decides.
Technically if I wanted my regenerate to go off before your regenerate, we would have a timing issue and initiative would decide, but that's a case where it doesn't matter and most people will ignore it. Cases where it matters are rare, but can be very simple or very complicated. It really boils down to the players though. If the players wish to know who's stuff happens first, initiative decides. However, each player always gets to decide for their own creatures.
For example: you have regrowth and rot on your goblin bomber, and there is the possibility if you take the rot first that you will kill my mage as well so I want my regrowth belt to go off first. I have initiative so I win the argument and use my regenerate first. You may then decide whether you want your bomber to die from rot or to regenerate however you wish. Even though our argument was based on you letting him die, you are not required to do so and it remains your decision. Not the player with initiative.
The only thing initiative decides is who decides first. Similar to a timing issue with enchants. Then that person can have as much stuff go off as they want before allowing the other person to handle their stuff.
