How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?
This is typically done using a segmented overlap add method or sometimes also refered to as a block convolver. 

Let's assume your block size if 512 (makes the numbers a little easier).


Chop up your impulse response into 32 blocks of 512 samples each. Zero pad each block to 1024 samples and FFT. You know have 32 filters $H_0(z) ... H_{31}(z)$
On each new input block: zero pad to 1024 samples and FFT. Keep the most recent 32 signal spectra around, so you have $X_N(z), X_{N-1}, ... X_{N-31}(z)$
Multiply the spectra and sum them, $Y(z) = \sum_{k=0}^{31} H_k(z) \cdot X_{N-k}(z)$
Inverse FFT the result: you get 1024 time samples. The last 512 are the "overlap". Store for the next block.
Take the first 512 samples of your inverse FFT and add the overlap from the previous block. That's your output.


Repeat steps 2-5 for each new block.