泊 was constructed phonetically(形声). The components are 水+白. There are a couple reasons why a character might be coined phonetically. It's possible that the word was already spoken by Chinese people, and when someone decided he wanted to write it down, he picked a symbolic radical and character that had a similar sound and combined them to coin a new word. That article is saying that 白 meant an acorn, and is a component of 泊, but that they have no connection (関係がない). It then explains the connection to shallow water.
To summarize, the etymology of the character is that in the Sino-Tibetan language family, the word for "shallow water" is related by meaning to "water" and had a similar sound with the word for "white."
You may have noticed that a few phonetic characters have phonetic components that are also very related in meaning to the overall character. That's probably because the people coining these characters didn't do it with the minimum effort possible. They actually put quite a bit of effort into coining them. According to "A Guide to Remembering Japanese Characters",
"it is possible that 白 also lent its meaning of white, since white water is generally associated with shallows. However, from an early stage 泊 became associated with shallow water suitable for an anchorage, then came to mean stopping place and eventually stop/stay in general."
Note how he said "it is possible" and how the source you came across doesn't mention this at all. That's because the proper etymology is just that the two words sounded similar.
For 泌, it says the character was coined by meaning(会意) and(兼) phonetic(形声) reasons. I've just explained what 形声 means. According to that source, 必 is a pictograph(象形) of someone pressing against two ends of a rod. It then says that 水＋必 refers to the water oozing out of the two ends of a pole that someone is pressing against. Actually, I'm not sure that source is correct. 必 is generally considered to have unclear etymology and "A Guide to Remembering Japanese Characters" says that it was originally a picture of a halberd between two poles. However, for 泌, that source mentions that in Chinese, its only meaning is "steady flow" which is wrong because looking in a Chinese dictionary, 泌 also means to secrete. This makes me question its accuracy. To be safe, I would say that 必 is unclear and 泌 was coined phonetically.