"Activate your core and keep it tight" is a cue I use whenever I coach any exercises that require a good, stable abdomen and lower back. Not all of my trainees really "get" that cue, though. You'll sometimes hear "tighten up like you're going to take a punch" as well, but that's a fairly violent clue for some people, and it can distract them rather than help them. Besides, my MMA coach says not to tighten up to receive a hit anyway.
I've used planks, Pallof presses, Turkish get-ups, woodchoppers, and other assorted exercises to get people to feel the abdominal activation and learn that it's not just holding your breath but keeping your muscles tighten while you breath. But it can take a while despite this, because most of these exercises have an element that will let you overcome a weak core, usually by powering right through the reps.
One thing I picked up from one of my clients is to use a 1+ second count at the area of maximum contraction with a band or tube-resisted variation of the exercise. You can't help but activate your abs if you are holding a band-resisted Pallof press at maximum extension. I prefer the band because the resistance is actively pulling you out of the position, and its easy enough to recover from if you start to lose it (unlike some weighted exercises - you can't recover from a lost TGU very easily, say).
So try this - add a 1-2 second hold at the maximum extension of a Pallof press and see if that doesn't get you supremely conscious of just what contracted abs feel like. I'm starting to use this cue and this method with all my clients, just to get them used to properly firing their abs.