I know that the pump has its own timer and it is nice to use what you paid for, however, think about this. The pumps internal timer has the ability to recover from a power outage. A mechanical timer (that controls your cleaner booster pump?) does not. Having those two pumps synced is critical for the well being of the cleaner pump seal. A power outage at just the right time for just the right length of time can leave that seal vulnerable to a "running dry" situation. That current controlled relay sounds like a good idea, but would that work in this situation? If it did, im sure it can only protect the pump from coming on. Resetting the timers would still need to be addressed (by a human) after the power loss, and if you were on vacation....
What we do is just run both the filter pump and cleaner with mechanical timers, or some sort of automation, and disable the internal timer. It was a good idea for the manufactures to integrate timers into their software. It appears that they just didn't consider the power outage scenario with another pump. The important thing (I think) is to have both the pumps controlled by the same type of timer.