Sprinklers on = no pressure in both sprinklers AND house
It could be a faulty safety pressure valve, f.e. used upstream of an electric/gas/oil boiler in the cold water inlet pipe.

In combination with the - assuming long - sprinkler lines/hoses, a sort of pressure (standing/reflected or other type of) wave could be established that opens this SPV periodically or permanently if the sprinkler is opened. 
The sprinkler itself could start that pressure wave if it is of a type that sprinkles intermittently.

Needing resonance, it would be only generated with the right matching length and cross section of hose/pipe.

The SPV could also be dirty inside. Many SPV have manual handles to turn/snap them open for a short moment in order to clean the valve.