It's not normal at all, but couldn't tell you specifically why it does that. Any sign of a misbehaving heater tells me it's time to replace. The on/off setpoints should be a degree apart and it usually takea a while to raise the tank water to that set point before turning off. It'll then take some minutes before dropping a degree or so again before turning back on. It works like the furnace in a home.
The heat from a pump output of second heater could mess with it that way. For instance, if you had a second heater right next to it. Or a second heater right next to a filter intake and the outflow was hitting this heater. But, all unlikely. I'd say she's telling you it's her time.