The "Artifacts" rules session seem to be clear that you first play
an artifact (place it in front of a Holy Place), then, from now on, use
it (rotate it to trigger its action), but it's not clear that this "use" can only be made during the Play Cards phase. I think this restriction applies, because:
From the rules session "Phase 2: Play Cards"
There are five different card types, which may be used in different ways and played in any order.
I noticed the "used"
Otherwise you could counter the Flamingo
by choosing to skip Play phase and still use the artifacts during your turn, or even use them before the Draw Phase, if there isn't a phase restriction.
I just need a confirmation on this thoughts.