Climb and Engagement

[White Noise]

There's something I've been wondering about concerning
the Climb ability. I've searched around and haven't found anything about this, so I figured I might as well ask.

The ability Climb says:
When moving up or down levels of terrain, (name of figure) may double/triple (depending on whether it's X2 or X3) their height.

My question is:
There is a Fyorlag Spider on a height 1 space and there is an enemy figure on a height 4 space next to the spider. Obviously they are not considered to be engaged. However, If the spider moves onto a height 2 space that is still next to the enemy figure (and for some reason has to use Climb X3 - say there's a battlement in the way) its height would temporarily become 6 (because Climb X3 triples height). Does it become momentarily engaged with the figure on the height 4 space? Furthermore, after moving onto the height 2 space and ending its movement, its height would revert to 2. Would it take a leaving engagement attack because it is no longer engaged?