Purchasing the token uses an outpost action, so that would be the end of your turn. The following turn, you could use the escort to move to a location and perform an action.
To be more clear, a turn is structured so that you may move zero or more spaces, then perform an action. Even if you were to use the escort immediately, you would not be able to perform another action in that new location until your next turn.
No where in the rules does it say you turn ends immediately after taking an action. Furthermore, escort doesn't take an action to use and doesn't even say it has to be your turn to do it.