I get confused by the terminology (is that my left, or coming from the left etc) but I presume you mean the preliminary cross-over of the laces. One way leads to a less secure knot and the other way should be secure - I don't have issues with laces undoing.
>>ndsipa+(OP)
Yes, if you do the initial cross-over right-over-left, then a normal 'bunny' knot, with the 'passive loop' on the right, it's secure.
They have to match. From all the "you're doing it wrong" posts and videos I can only assume that everyone (else) is learning left-over-right for the initial twist, and then right-loop for the main bow, which of course slips.