Oh I want to know the answer to this as well. Sometimes my toilet will flush itself while I'm having a shower, and if I'm not paying attention I get cooked.
Slow leak makes sense if it's filling the tank for a couple seconds. It doesn't make sense if yours is full flushing. Don't know what would cause that.
The toilet flushes because the bowl is filling up. That's what causes it to flush. Why the bowl is filling up when you shower... I have no idea. Sounds bad though.