I assume you mean blinking red boiler light.
This is a blocking alarm that goes on when the pump runs for longer than 1 minute. It's meant to avoid burning out your pump if the automatic refill is not working (see section 5.7 of the Mini users manual).
The flow rate of the Ulka pump in the Mini under 0 pressure is about 0.65L per minute. So it takes a little under 2 minutes to refill the 1.1L boiler if it is completely empty. That's the reason the blocking alarm activated.
I prefer to half refill my boiler by filling through the removed vacuum breaker on top, to avoid exposing the heater with no water (but as you say, the on/off button + hot water button is even better if you want to refill without the heater and without removing the vac breaker). Still, if you completely drain and turn on the machine, it is most likely the heater coils on the bottom of the boiler get covered in the first 30 seconds after restart (i.e before it has heated fully), so I doubt you can really do much damage.
In other words, sleep well. Likely no harm was done.
