Hi James,
Hope you've been well and here's my 2cents I'm no expert on lures but I don't think you are doing anything wrong even if you cannot hook up on every hit you can feel.
Flathead are relatively easy to catch because they ambush prey and thus are not as selective. I guess they may lay in wait for a long time before a meal presents itself so that makes them less fussy. Also, they have a big mouth and engulfing an entire lure is easy.
Bream are much more inquisitive and mobile. Sometimes they will follow prey and examine it before deciding to eat it. They have small mouths and won't swallow a lure deep, unlike a flathead which makes hookups less likely. In my experience, bream don't really spit lures out all that quickly. They are likely to pick it up and carry it away from the competition but the lure can become dislodged if there is line tension. Being a more active fish, they may chase lures and short strike at the tails only etc. leading to no hook ups but continual bites. Striking immediately might lead to a hookup (mouth or foul) but more often than not there is no weight on the end.
Tentatively regarding jews, the common belief is that they spit out lures almost as fast as the hand can strike. In that case, timing is everything. If there are any jew experts out there, please feel free to add to this thread
I generally strike at a hit but not when it feels like the hit was stopped by my line tension. In that case I continue to work the lure and entice another strike and hope that the fish hooks itself by loading into it. If the hits are persistent, it is more likely that really small fish are harassing the lure and may not be worth the time so moving to a different spot might be better.