Polyp extension is most likely in response to the acknowledgement of a food source in the water column. Yes, turning flow off may be a Pavlovian response as well. I don’t think anyone can definitively say.
Coral are stationary creatures (as an oversimplification). Placing a bowl of food 10 feet away from a quadriplegic dog may evoke a response but will not feed the dog.
Water movement, especially in SPS is critical to their health. This is a well known and researched fact and the science behind it is readily available.
Consider a train: It takes a lot to get it started. Once it’s started it will pick up speed and move briskly. If you choose to slam on the brakes for 15-30 minutes a couple times a day, Each time the train will need to begin the process of getting back up to speed again. It won’t get very far in a day.
People focus so much on ratios and certain numbers on here and completely discount arguably the most important factor in this hobby. Stability. Creating an environment that is stable is key. By creating constant rapid changes (flow, no flow, moving corals, rapidly raising alkalinity of calcium to different levels to try and invoke faster growth, changing lighting spectrum, dirty hands in the tank, etc) you’re doing more harm than having the “perfect” alkalinity or “perfect” Ph.
Here are the most common options:
Option 1: Turn off flow, wait for poly extension. Use a syringe or other tool to spot feed each coral by gently spraying the food over the extended polyps. The entire process will take 10-15 minutes and there will be no I’ll effects.
Option 2: Turn off your return pumps using a very common “feed mode” feature associated with pumps and controllers. Optionally create a feed mode setting for your power heads or circulation pump that reduces their speed. Add your food to the tank and allow the power heads to move the food around your corals for 10-15 minutes before turning the return pump back on.
Option 3: Don’t bother feeding your corals because if you have sufficient bio load and are already feeding your tank, your corals probably don’t need the additional food.
The only corals I have seen marked improvement in with feedings are NPS, Duncan’s, and Acans. It has been a waste of time and money for me beyond that. I think if we could look closely at many many medium-to-well stocked mature tanks that broadcast feed we’d find that these extra foods and aminos and things are not doing anything magical over just adding a little extra fish food.