Well, here's what I see...
1. Tap water. Every get a reading from a TDS meter on your tap water? That may be the problem right there. It may not be that bad, but that combined with your temp. spike may have been enough to let the HA take hold.
2. Temp. spike. Was it just a spike, or is it holding at that temp? Algae loves higher temps.
3. NO3 & PO4. Algae can take up those nutrients very quickly, so you could have high levels of NO3 & PO4, but they test lower because the algae is pulling them out of the water.
In the States we have vending machines that dispense RO water outside of grocery stores. Maybe something to look into. Or a home RO/DI unit would be even better.
I wouldn't worry too much about the live rock, it should be okay.