The magnet was the cause, at least after you "pushed" the blue spots around.
There is a very fine grid behind the glass of a CRT.
If this becomes magentized, it will disturb the electron beams that are used to create the image on screen.
Depending on which end of the magnet you used, the magnetized areas either pull or push the electron beams off course. In either case, the electron beams don't go where they belong, and you get wrong colors.
Modern CRT TVs had built in degaussing coils to neutralize magnetized areas. Yours either didn't have them, or they weren't working right.
TV technicians have large coils that generate a changing magnetic field using alternating current. These magnetize and demagnetize the whole surface repeatedly at 50 or 60 Hz(power line frequency.) Bringing such a coil close to the CRT evens out the magnetization. Slowly moving the coil away from the CRT reduces the magnetization. When you get far enough away, the magnetization is pretty much neutralized, and the picture should again be clear.
Image of a CRT screen that needs degaussing: