CTR DRBG dependent on request size?

I am trying to understand the CTR DRBG specification in NIST SP 800-90A. It seems slightly different to a pure stream cipher in that the key and counter are reset after each generate call using the output pseudo-random bits. I understand that this is to provide backtracking resistance.

My question is, does this imply that the output bits produced by the DRBG are dependent on how the requests are 'chunked'? i.e.

$$Generate(state, 8) || Generate(state, 12) \neq Generate(state, 12) || Generate(state, 8)$$

...or have I not understood the specification correctly.

You are correct. The $Update$ function is called after each invocation of the $Generate$ function, and this does mean that chunking affects the output. Changing both the key and the nonce of an $AES-CTR$ key stream generator to uniformly selected (pseudo) random values will, of course, make the resulting key stream uniformly independent from what it would have otherwise been.
However, it might be noted that the first $8$ bits of $Generate(state, 12)$ equals the full $8$ bits of $Generate(state, 8)$.
It should be noted that a $DRBG$ is primarily to be used as a replacement for a $TRBG$ (true random bit generator). It is not designed to be used as a stream cipher (which must support chunking) or as a key derivation function (which might support chunking). In particular, the NIST SP 800-90A specification explicitly forbids instantiating a $DRBG$ with the same state twice, which by itself makes it impossible to use it as a stream cipher or key derivation function.
• Good edit, I did of course already upvote. I would consider this answer even better if there was a description on how the state (in \$10.2.1.1 of the standard) is affected by requesting differently sized chunks. So that would be the vector V and possibly the reseed_counter of course. – Maarten - reinstate Monica Nov 21 '15 at 13:58