Yeah, that sounds weird as hell. Post pics of what you got. And $150 to "fix" it, is complete robbery. For $150, I could buy all new joysticks, all new buttons, all new wires, a new iPac and dinner for my family.
^This
DO you know what type of encoder is being used ? IT's really hard to help without knowing more about it - take some pics of the existing wiring and pieces and we'll be able to help more.
Figure in most case the joysticks will be wired with 8 wires (2 to each direction) 1 wire hooked to the NO and 1 hooked to the common connector on the switches ( Unless you have Japanese Joysticks which will only have 5 wires ( 1 for each direction and 1 for the common ground) those wires will go to the encoder (depending on which type of encoder the exact position of the wire will vary) Then the encoder will run to the PC ( if using a PC in the system) etc.
SO very hard to detail what you need to do without knowing what specific parts are being dealt with -- so pics and some more info would help. Also with the wiring the way it sounds like from your description it might be easier to just start from the begining to ensure something weird is not happening ( and if the guy asking for $150 to fix it is the guy that originally wired it up I'd be inclined to pass !) but again hard to say without a bit more info to get started.
EDIT : Just saw your pics and all I can say is OUCH !!
As I thought might be easier to start from scratch - DO you have a soldering iron and know how to use it ??
Quick note on what I see in your second player pic :

FIrst off several wires missing connections and several ground wires running to wrong connection - IN the pic each Joystick direction should have 2 connections to it 1 for ground ( this is the orangeish wire running to the upper connector on each switch as it runs from 1 switch to the next which is fine but all 4 directions should have one of these connections (see red circles and X's I put in the pic)
SO looking at the pic you can see on the right side the red circle on the switch with a 6 on it has that orange wire coming from the switch to the left correctly (from the top ground of that switch to the top ground connection of the next switch but then runs to the wrong connection on the next switch ( see red X ) athat should go to the top ground of that switch.
The ground wire runs in a loop from one switch to the next always on the top Ground connection of the switch (that way the 1 wire grounds all switches) and then runs back to the ground connection on the encoder)
THen you need one more connection from each switch back to the encoder spot for that direction ( See the red and Yellow wire in the pic for correct connection that should run back to the encoder - seems red is UP and yellow is Left - but the other 2 are wrong (either have a ground connected to them or no wire at all ??)
Same goes for the player buttons -- Each should have one connection to the current GREEN wire that runs from 1 button to the next and then that goes back to the encoder hokked to a ground location and then each button should have another wire (different for each button) that runs back to the encoder connection for that button (ie. from button 1 to encoder location for P2 button1
Hope you can read that !! but to quickly summarize best bet is to start over with the wiring -- to do that run one wire from the encoder ground to each switch on the joystick and/or buttons top ground location ( so this one wire can run to all 4 joystick switches and each of the 6 buttons to the same connection on the switch and then to the next switch (so the 1 wire will connect to all 10 switches on the top connector) THis will make a ground loop) or you could run 1 wire to each of the 4 joystick connectors and another wire to each of the 6 buttons and then connect those 2 both to the ground connection on the encoder -- either way will work but you need 1 connection from each of the switches that links back to the ground on the encoder.
THen after you have each switch grounded you want to run 1 wire from the encoder location for that button to the corresponding switch and connect to the NO (normally open) connector - so for example the Red wire runs from the joystick up back to the encoder Player 2 Joystick Up encoder connection, the Yellow Wire runs from the Joystick Left switch NO connection back to the encoder P2 Joy Up encoder connection -- etc. etc. etc. for all 6 buttons and 4 joystick directions.
It really is easy if you start at the beginning rather than trying to figure out what is currently going on as right now that white wire, green wire, orange wire, etc. are running to several connections in different places which should not be !! Each switch needs 2 connections to the encoder 1 for the NO connection that goes to the encoder at the corresponding input (ie. joy2 Up, Joy2 Down, Button 1, button 5, etc.) and 1 for the ground (these can be a single wire run from 1 connection to the next always on the ground connector or can be up to 1 wire directly to each connection back to the encoder ground)