I caught both Salmon and the King salmon on the first of september,and i have to say they're easy!
Im sure it depends on how your waterfall is placed,but in any case,all you need to do is save and continue in front of it,then if you see a large shadow that's the salmon,if you see a huge one that's the king salmon
What took me a long time to get is the char,i probably fished around 20 salmons and 6-7 king salmons before i found one
I got my king salmon today after a ton of regular salmons. I think I'm quite fortunate with my waterfall placement - there's a tiny bit of land just above the waterfall and with some saving and continuing, there's fish there all the time.
(what luck I have in waterfall placement I lack in fish-catching skill; I panic and press A too early all the time)
About time, well, i did check everytime i could without any fish appearing.
I caught those salmon and the king around 2~3 pm... I think, if not a bit earlier but not much, maybe 1~3 pm is the closest range I could give, you can try those hours maybe they do appear more at that time, after those I haven't seen any shadows in the waterfall.
I checked in the nights too these days, and I haven't seen any shadow, so I dont know if it really is easier in the nights, maybe it depends in the game and town, or w/e. But for me, no luck in nights.
I just caught both of them! Yay!
It was 11 am and raining. I saw a shadow so got my wetsuit and swam over to the tiny strip of beach. I caught the salmon. Then, RIGHT after the "I wonder what my encyclopedia has to say about my new catch" thing appeared, a king salmon appeared! And I caught it as well. What luck!