They are next token producers. I would only call it a predictor, if it's trained to predict tokens (ie just after pretraining).

Just like humans produce one word after another when they talk, but they don't generally try to imitate other humans.

Don’t people pick up language, vocabulary and dialect from those around them? Perhaps it’s subconscious but humans are imitating other humans all the time?

It's a mix.

Yes, you imitate how others speak, but when you are trying to solve a problem, you don't try to predict how others would complete a text.

(Well, unless you follow 'what token would Jesus pick?' / 'what would Jesus do'.)