When multiple characters in a combat roll the same initiative, PCs take their actions before NPCs. As it says in the book, "Earthdawn is a game about heroes, after all!"
PCs who go on the same initiative may choose what order they wish to take their actions in.
There are a number of abilities that require the adept to go on a higher initiative than their opponent. These are phrased, RAW, as "the adept must have a higher Initiative" . An initiative tie does not count for these purposes.