I have a ceiling fixture that is controlled through 2 3-way switches (power comes from the fixture not to one of the switches). in the same room, there is a set of wall light fixtures that are tied to one switch installed next to one of the 3-way switches (the power was coming to the single pole switch until we finished the basement and the contractor damaged the wiring without noticing). can I power the single pole tapping power from the 3-way switch? will the wall fixtures be tied to the ceiling fixture? I did a trial but the operation was reversed (i.e. I can only turn the wall lights on if the ceiling lights were off).
Most likely, the hot wire is coming first to the other 3-way switch. From there, power comes on one of the two travelers to the 3-way you're working with. You've probably connected your new switch to one of the travelers. I'd bet if you switch the other 3-way, the light will come on and off together.
Without the hot coming to this 3-way, you cannot have independent operation of the new switch.