It's actually pretty clear that Jeremy Corbyn voted to stay, as he called for people to do. Like Corbyn, most Remain voters believed that the EU is far from perfect, but that for all that it was a better choice than Brexit.

The fact that Corbyn was actively saying this probably influenced many wavering Labour voters to opt for Remain. If he'd come out as an uncritical fan of the EU it would very likely have pushed many the other way. Aside from anything, he would have been seen as another lying unprincipled politician. Critical support of the EU made sense. If the choice had been between Brexit and EU adoration, the margin for Brexit would have been far wider.