You need to program the remote for your TV. Channel changing is done by the cable box not the TV so that does not prove the cable box remote is programmed for the TV. In some cases the same is true for volume.
If the remote properly turns on or off the TV, that is an indication the remote is programmed for the TV. For other functions, you have to press TV at the top of the cable box remote, if the CABLE light is flashing when the remote keys are pressed, then you are sending instructions to the cable box, not the TV.
Since Time Warner uses several remotes, you may need to go to the Time Warner web site or store to get instructions on how to program your remote for your brand of TV.