I can confirm StarFallArmada's & Thoumsin's statements : Friendly AI's fire their Novaliths at your systems, although other empires were also targeted.
These were systems that had been established for a long time - even before the AI had started building Novaliths.
This is IMHO is a new bug, friendly AIs in Trinity did not target your core worlds.
Polistes is also correct, but only for newly colonized planets where the super-weapon fired beforehand - I've had that happen (with my own Novalith) while playing Trinity.
The only counter to this new bug are SBs + Aux Govt at every planet, including your core systems.
Fortunately, in my case I had the economy to fund it and therefore could afford the 100% trade loss of the Novalith impact.
The AIs favoured specific planets, especially those that had an artefact.
Oddly enough, my empire didn't seem to mind (too much) that it was being bombarded, surely that should have a negative effect on the diplomatic relationship?