Shadow cards are dealt at the beginning of the combat phase, before enemies attack. Striking Tentacles will also trigger their Forced effect, discarding an encounter deck card when they attack (for the other kinds of tentacles, the Forced text only triggers when YOU attack THEM). So, with a Striking Tentacle, it'll look something like this:
1) Deal shadow cards to all enemies at the start of the combat phase.
2) Decide which enemy will attack first. Declare defender (or let it go undefended).
3) If that enemy is a Striking Tentacle, discard the top card of the encounter deck. This attack becomes undefended if the discarded card is a Tentacle enemy or has a shadow effect printed on it.
4) Reveal the shadow card that you previously dealt to the Striking Tentacle and resolve its effect.
5) Resolve attack damage.
Rinse and repeat for remaining enemies. If the tentacles are Grasping or Thrashing Tentacles, you won't discard any cards from the encounter deck until you get to the next step of the combat phase, where you declare your own attacks.