I point up, down is uncomfortable for me. It does up into the waistband. When my dad gave me my first jock at 13 he said to point up- so I always did. And if I get hard - it doesn't hurt as much.
I have 2 unlined board shorts for the beach. I use a Bike swimmers jock under. I also have a blue Cellblock 13 but it doesn't have as much support as the Bike. https://www.bikeathletic.com/collections/jockstraps/products/swimmer-jockstrap-white
Back in school days we had those larger nylon swim trunks that today would be considered "square cuts" and didn't wear them tight like the lycra suits are worn. Many of us that were jocked underneath would let the back waistband show above the swim trunks. I never recall saying anything or...