Noises generated by OpAmp driving 50 ohm load
Some things to think about...


Are you sure that you are properly measuring the signal in the power supply lines of the OpAmp? Improper placement of the scope probe ground could account for all of the signal that you see on the power supply lines.
Do you have proper power supply bypassing on the V+ and V- pins of the OpAmp? If not apply some good quality ceramic bypass capacitors to your circuit.
Did you build your circuit on one of those proto boards where bunches of wires plug into rows of holes? These things will have coupling between adjacent rows of contact holes and your plug in wires. Try building on a more normal circuit board (proto wired or PCBA).
What did you do with the other OpAmp(s) in the package? If you left it(them) all open and unconnected this may very well be root of the problem. Spare OpAmps in a package need to be wired up so that they do not cause problems.