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I tried Google, and I couldn't find the answer, so I have to have ask this question here. Is this correct?

one millionth of a billionth of a trillionth of a second.

I can write one 'undecillionth' of a second, but I don't feel that many people would imagine the weight of the said term like they can with millionth to trillionth?

Note, "negative" as used in this answer is interchangeable with "minus". Thanks to a number of commenters pointing this out, NGram Viewer and Google search both show "minus" as being more frequent than "negative". "Negative" may be more common in formal use.

Exponentiation such as you've shown is usually said, in your example either:

Ten raised to the power of negative 36

or

Ten to the power of negative 36

or

Negative 36th power of 10 (less common)

or

Ten to the negative 36th power

or more casually as:

Ten to the negative 36th

Notice that in some cases we usually use the cardinal number (36) whereas in other cases we use the ordinal number (36th) when referring to the exponent. Although what I've listed are the more common ways, the cardinal and ordinal forms aren't absolutely universal. For example, you may hear:

10 to the negative 36

However, in my opinion this is much less common.

_

The exponent is usually shown as a superscript to the right of the
base. In that case, b^n is called "b raised to the n-th power", "b
raised to the power of n", or "the n-th power of b".
Wikipedia:
Exponentiation

Notice how it's said in this Khan Academy video, it's said in the shorter way I described, ie., he says ten to the twenty-third.

Specifically in your case of seconds, it would be said:

Ten to the negative 36th seconds

or

Ten raised to the power of negative 36 seconds

or

Ten to the power of negative 36 seconds

or

36th power of 10 seconds (somewhat less common in my opinion, I don't recommend this)

Is this correct?

one millionth of a billionth of a trillionth of a second.

Yes, that's correct, and depending on how you want to convey your information, that may be preferable to you. In one sense it puts into perspective how large or small of a number it is. People may be able to imagine numbers as big as a million or billion, so you can express it in terms of these units if you want. Equivalently you could say:

One quintillionth of a quintillionth of a second

It's up to you how to express it.

Finally, about the word "undecillion" or "undecillionth", I would advise against using that unless comprehension is not important. Firstly, it's an uncommon word. Secondly, as shown by the dictionary definition below, it can be two different numbers, I assume as a result of the differences between the short and long scales which (historically) separated Europe and the US.

undecillion
a cardinal number represented in the U.S. by 1
followed by 36 zeros, and in Great Britain by 1 followed by 66 zeros.

Random House Unabridged Dictionary