HMAC_DRBG Generate Process: requesting N bytes at once different from requesting N bytes in total? Am I correct in assuming that HMAC_DRBG would return different results if I, e.g. first request 4 bytes followed by a request of another 4 bytes instead of asking for 8 bytes at once?

It seems that in NIST SP800-90A chapter 10.1.2.5: Generating Pseudorandom Bits Using HMAC_DRBG first the K and V values are changed, then the requested number of bits is generated (changing just V), and then the K and V values are changed again. Besides that, leftover bits get chucked away as well.

Isn't it a strange property for a DRNG to return different value if DRNG(4) || DRNG(4) != DRNG(8) if the DRNG is not reseeded in between? Do other DRNG's have the same kind of property?
Yes, you are reading this right. The requests for random value from NIST 800-90 drbgs perturbed the state.  If this is a problem you can add a layer that optionally buffers values and always makes constant size requests.