There are parts of radicals that can help you remember them, but that doesn't always directly dictate the context. Rather, that it's how kanji itself is used that is subjective, not radicals. Radicals aren't everything. They're pieces that make the kanji, can help provide information about the possible meanings to the kanji or the word that is used, but they don't speak about which pronunciation to use.
Remember, sometimes kanji isn't just used based on onyomi or kunyomi readings. It's not always binary. Sometimes there are other readings that aren't defined individually in the dictionary. Yet when it comes to there being onyomi/kunyomi readings identified in a dictionary, you can have several of each type. That's why context, how kanji is used, tells you more about what the word actually is and what it means. That's really how you know which pronunciation is used.
It could also be said that each pronunciation is related to some of the specific meanings or something similar, which may offer you a clue about which pronuncation/reading is used. Add to that, there may be some historical basis to that word and the kanji being used. Especially when it seems time hasn't been so kind to it. The limits of the radical just merely provides the structure (no pun intended) for the kanji. It doesn't provide for every specific meaning but the one main one when it may be combined with other components to make up the kanji. The whole kanji, and use with other kanji/okurigana gives more dynamics for different meanings.
In one example, 家 has several meanings. The radical here doesn't make any difference. It just makes up the fundamental basis of the kanji, basically drawing a picture. The meaning of the kanji houses (pun intended) different ideas that may be related to the picture in some way, and the radical serves to be a part of its meaning. But it doesn't cover every specific meaning. You need other kanji/okurigana to help figure out the word.
The meaning may also contain emotional attributes. If you said it was 「いえ」, this is kind of cold, maybe formal. Direct. The meaning attached to that word describes the physical building. A house.
If it were 「うち」, this is softer, more sentimental. it describes a place. The meaning for this is "home". This would make sense, yes? Probably most of the time the word itself would rather be written in hiragana, so you'd less likely see the kanji used for this context, but it's still valid.
There's also other meanings for the kanji which may require a combination of other kanji. So the main onyomi/kunyomi pronunciation you use may be subjective with respect to what is combined in it. Another onyomi for 家 is か. One word using this, such as 画家「がか」, describes a profession. In this one, the meaning is towards one's occupation as a painter.
There's another, using the や pronunciation. For example, 家賃 「やちん」. Another carrying a related meaning, but different word with respect to this for example is 借家「しゃくや」. If this were a pattern, you'd likely have a very good guess that using や for 家 is related to something to do with renting. But sometimes や is also used for something different, such as an occupation or place that normally could've been か. Exceptionally, maybe more towards a characteristic, if that helps you think of it.
The functional basis of a radical may be used for people's mnemonics. Regarding the radical for 家, one can illustrate a roof of some type. As a concept, the idea of the kanji relates to something responsible for putting a roof over ones head. As we can also see, it doesn't necessarily have to be literal. Things such as occupation, a transaction such as rent, are things you can imagine have to do with what part of your life keeps you under shelter. That would generally be what the radical may have to offer, but it stops short at providing nuance.