If a clause makes sense on its own, then it is an independent clause (an independent clause will always have a subject and a verb). You do have to put a comma before "but" if it precedes an independent clause.
For example:
Tom not only forgot his wallet, but he also forgot his phone
In the above example, "he also forgot his phone" makes sense on its own, thus it is an independent clause and must be preceded by a comma.
Now take this example:
Tom forgot not only his wallet but also his phone
In this example, "also his phone" does not make sense on its own, thus it not an independent clause, and no comma is needed.
For your last sentence, you are correct to omit the comma, because "but also kind" doesn't make sense on its own, and is not an independent clause:
Tom is not only smart but also kind
However, you could change the sentence to make it into an independent clause, in which case you would need a comma:
Tom is not only smart, but he is also kind
Only this one is correct:
Not only were they tall, but they were also strong.
I think, we have to do inversion every single time a sentence or clause begins with not only. There is no exception to this rule. I think of this type of structure as a pattern that never breaks and one you simply should commit to memory.
One more example:
Not only do I have to now install the operating system again, but also buy a new computer.
It seems to me that we typically do inversion in English when a sentence or clause begins with a negative word or phrase (the operative word here is begins). One of the most common words of that group that immediately springs to mind is rarely.
Rarely do you see people using desktop computers nowadays. Most people prefer laptops to them because of their better portability characteristics.
However, there is going to be no inversion when not only, or rarely for that matter, is found between the subject and the verb:
I not only have to now install the operating system again, but also buy a new computer.
Best Answer
The parallelism rule doesn't say that everything that satisfies the rule is correct and nice: it just says that everything that does not satisfy the rule is wrong.
You can divide a sentence up in lots of different ways so that each clause contains the same grammatical components:
All of these satisfy the rule: not all of them are equally nice. For me, the second example sounds nicest so that's the one that I would use.