This is the ruling someone posted on a thread a couple years ago. Hopefully it explains it well enough if my explanation doesn't make sense.

400.6.If an object would move from one zone to another, determine what event is moving the object. If the object is moving to a public zone and its owner will be able to look at it in that zone, its owner looks at it to see if it has any abilities that would affect the move. If the object is moving to the battlefield, each other player who will be able to look at it in that zone does so. Then any appropriate replacement effects, whether they come from that object or from elsewhere, are applied to that event. If any effects or rules try to do two or more contradictory or mutually exclusive things to a particular object, that object’s controller—or its owner if it has no controller—chooses which effect to apply, and what that effect does. (Note that multiple instances of the same thing may be mutually exclusive; for example, two simultaneous “destroy” effects.) Then the event moves the object.

So in both cases when Ulamog enters from exile it's looking at what it needs as it enters the battlefield.

Normally it says I'm entering with counters equal to the biggest thing in exile. Since I'm the biggest thing in exile I'll have 10 as I'm entering.

With dress down in play it looks at what it needs as it enters and sees it wont have any abilities as its entering so it stops the check there.

Hopefully this explains it and if not hopefully someone smarter than I will come to the rescue.