The start threshold does not make much sense for capture devices; just set it to 1.
The hardware fills the capture buffer continuously, but raises an interrupt only at the end of each period. When ALSA is waiting for some data to be available (in poll or in snd_pcm_read*), it will not return before avail_min frames are available. However, this check is done only at the start of the function, or when it is woken up by the interrupt.
Therefore, if you do not want to wait for too long, you have to make the period size short enough.