I have only heard the phrase pronounced 'ALA DAL'ONA, but have seen it spelled in all sorts of ways, both in Arabic and in Latin letters.
As a child, I was aware of the phrase only in the context of the well-known refrain, sung by almost every Lebanese singer (Sabah, Fairouz, Nasri Shamseddeen, Wadee' Al-Safi, etc.) as well as some Syrian singers (there is even a humorous rendition by Duraid Lahham).
Up until recently, and precisely because of the popular refrain, I thought that DAL'ONA was a place name, and that the musical couplet was indigenous only to Syria and Lebanon. The phrase sounded like "Let us go to Dal'ona."
Looking through the Internet, however, I found out that, one, DAL'ONA is a form of dance music (actually dance and music), closely related to the Dabka, and, two, that it is just as well known in Palestine. Here is a link to a page with releveant ethnomusicological information:
"Dal'ouna, a strong icon in traditional dabka, is one of our [Palestinian] most well known dances, with its powerful steps, energetic leaps and spins. Al shabab add a unique and contemporary style to Dal'ouna, while keeping its tradition strong. It is a sure crowd pleaser.
Al Yarghoul is also an instrument used to play Dal'ouna. It is often compared to the sound of bagpipes. Al Yarghoul adds a special accent to any song, yet when it comes to al dabka, al yarghoul gives the dabka song an extra boost of energy."
So what does "ALA DAL'ONA" mean? I believe it is a phrase whose "meaning" is almost purely musical; i.e., it has no significant cognitive content amenable to translation, but merely serves to establish a quick dancing rhythm and to form part of a rhyming couplet.
If you insist, you can translate it as "On to the dal'ona," or "let's dal'ona," if I may dare turn it into a verb.
The subject is certainly ripe for further research. I would love to hear more about it from the other members.
Note: I could not read the term that you posted, only the "explanation". are you using a Mac?