its 60 seconds after it becomes their move, when they disconnected when it's not their turn. The 60 second countdown begins when it's their turn in this case.
If they disconnected in the middle of their turn, then they have 60 seconds to reconnect.
So the first scenario, it is longer than 60 seconds.
There can be serious server issues affecting connectivity that could mean that 60 seconds isn't long enough. For rapid games, it's more appropriate to extend to longer.
When players get disconnected and then after around 30 seconds they are forfeited for not reconnecting in time. There needs to be a longer time given for a player to reconnect or no time limit at all, in my opinion.