Fan CFLs flicker when off - unsafe?

When we bought our house a few years ago, we replaced a chandelier light in the living room with a ceiling fan. This weekend, I finally got around to installing a light kit on the fan. That went smoothly except that when the CFLs that came with the light kit are turned off, they flicker dimly. I have checked the connections between the wires and, though I could be persuaded otherwise, I am pretty confident a loose wire is not the problem.

The fan isn’t controlled by a pull chain but instead came with a four button box with which I replaced the light switch at the same time we installed the fan. The electrical box only had one white and one black wire coming out of it. I understand that new construction would possibly have two black wires to control the fan. This house is 100 years old and didn’t even have a ground wire in this electrical box. Connecting those wires to the control box seemed to work fine.

Unlike the fan, the light kit does have a pull chain. In addition to that, there is a power button on the fan control box in the wall. Finally, there is also a button in that box that turns the light on or off. All three of these switches/buttons need to be on for the lights to be on. Both the power button and the pull chain appear to function as physical switches: when they are set to their on or off state, they will stay that way until a person changes them. The light button is not. If the lights are on and the power button is pushed, the lights (and the fan) turn off. If the power button is pushed again, the lights do not turn on but do flicker. At that point, hitting the light button will turn them on.

To be clear, the lights flicker in this state only:
chain: on
power: on
light button: off

From what I’ve read online, it appears likely that replacing the CFLs with LEDs or incandescents will probably stop the flickering. I’m wondering, though, if the flickering is evidence of something unsafe.

Not unsafe, but may shorten the life of the CFLs.
What is happening is this: The fan control is allowing a small amount of current to flow though the lamp circuit, causing the CFLs to blink. This is very common with X10 and Z-wave dimmers, and is simply annoying, but not dangerous.

LED bulbs will probably do the same thing.

Thanks. I’ll definitely replace those bulbs with something else so I don’t waste the ones in there now, then.

I’ve got a couple other fixtures that I want to put LEDs in. So I’ll buy a couple for the fan but keeping in mind they may wind up somewhere else in case they flicker, too.