Bright auroral emissions during geomagnetic storms provide a good opportunity for testing the proposal that substorm onset is frequently triggered by plasma sheet flow bursts that are manifested in the ionosphere as auroral streamers. We have used the broad coverage of the ionospheric mapping of the plasma sheet offered by the high-resolution THEMIS all-sky-imagers (ASIs) and chose the main phases of 9 coronal mass ejection (CME) related and 9 high-speed stream (HSS)-related geomagnetic storms, and identified substorm auroral onsets defined as brightening followed by poleward expansion. We found a detectable streamer heading to near the substorm onset location for all 60 onsets that we identified and were observed well by the ASIs. This indicates that substorm onsets are very often triggered by the intrusion of plasma with lower entropy than the surrounding plasma to the onset region, with the caveat that the ASIs do not give a direct measure of the intruding plasma. The majority of the triggering streamers are tilted streamers, which extend eastward as their eastern tip tilts equatorward to near the substorm onset location. Fourteen of the 60 cases were identified as Harang streamers, where the streamer discernibly turns toward the west poleward of reaching to near the onset latitude, indicating flow around the Harang reversal. Using the ASI observations, we observed substantially less substorm onsets for CME storms than for HSS storms, a result in disagreement with a recent finding of approximately equal substorm occurrences. We suggest that this difference is a result of strong non-substorm streamers that give substorm-like signatures in ground magnetic field observations but are not substorms based on their auroral signature. Our results from CME storms with steady, strong southward IMF are not consistent with the ~ 2-4 h repetition of substorms that has been suggested for moderate to strong southward IMF conditions. Instead, our results indicate substantially lower substorm occurrence during such steady driving conditions. Our results also show the much more frequent occurrence of substorms during HSS period, which is likely due to the highly fluctuating IMF.