RGB LED lighting controller
It seems "possible to likely" that the relative polarity of the two controllers is reversed.
 Whether the controllers and strips will work together depends on how they the strips are wired.   

If you have the +ve and -ve ends of 3 colours of LEDs available (R+, R-, G+, G-, B+. B-) then you can probably just " turn the LED strips around end for end". BUT it is more likely that 


One controller expects common Anode LEDs where the +ve Anodes are joined together and you drive -ve cathodes separately - so you get terminals Common+, R-, G-, B-. 
The other controller expects common Cathodes with -ve Cathode end of LEDs common and +ves brought out so you get terminals common-, R+, G+, B+.


IF this is the case then the two systems are incompatible without either extra equipment.
 In some cases cutting and rejoining of the internals of the LED strips may be posisble if they have used separate R, G, + B LEDs but in most cases the RGB is liable to be in one LED package and cannot be re-arranged.

If you can provide specific controller and LED strip brand and model references and ideally web links we should be able to suggest a controller design that would do what you want OR be able to suggest that you quit while you are behind. 

Obvious in hindsight advice: When buying such equipment one should either know what is involved and be sure re compatability OR have a supplier guarantee that the components will interoperate and  that you have right of return if this is not the case. (This is a lesson that your client needs to learn and you may or may not be in a position to "safely" teach it to them :-).)