From the rulebook:
"If a player loses a game and there are at least two other players remaining, remove his player marker and all of his cards from play (and discard any opponent's cards that were on them).
Remove his sites on the adventure path in numerical order, and replace each with an opponent's corresponding site, in counter-clockwise order starting with the player on his right.
The other players complete the losing player's turn."
Since it says to "complete the losing player's turn", I would interpret that to mean any phases that are left would in the losing player's turn would still occur. Otherwise, I would have expected it to say something like, "Immediately start the next player's turn."