Common Element

Your tube going to the drain line is yours alone.

After it connects YES.

In CA, if more than one but not all share an element, it might be exclusive use common area. In SC, it might be called something else like limited use common element.

Your documents might say who's responsible for this element. Or they might be very vague about it. Apparently, SC has laws about condos that might help.

it is common in 'hi-rise' construction to have a 'leader' for A/C condensate as opposed to a tangle of individual tubes leading to ground level

It very likely is a code violation because the HOA adamantly insists that all units in this development have separate AC drain lines. Mine does not. If they admit that I have a common drain line, the master deed says they have to reimburse $382.50 to me for a repair of a common element.

The master deed says: The ASSOCIATION, at its expense, shall be responsible for the maintenance, repair and replacement of all of the common elements. My interpretation is that I paid to have a common element repaired
(the shared AC drain line) which is the responsibility of the Association not mine. They should have paid to have it repaired, not me.
The condo building has a ground floor and a second floor.

The AC drain lines don't have to be separate but if they are not separate,they are common and if they are common they are the responsibility of the Association. In the past, there have been claims by other homeowners that they have common AC drain lines only to be shot down by the Association and the property management co. In my case I happened to hire a plumber who knows when the homeowner is responsible for a repair and when the Association is the one who has to pay. He told me that without a doubt, the Association is responsible in this case. He had to unclog the line which made it necessary to cut an opening in the wall so the spot where the lines join together is easily visible. And yet, the Association continues to ignore the fact that the drain lines are common. At this point, I'm waiting for an opinion from the Association attorney. But to me, this seems to be a simple open and shut case.

When the plumber told me that I would not have to pay for the repair due to the fact that the AC drain was a common line I said but it's only one other unit using the drain line. He said that's all it takes.
The plumber has been in business for 45 years.

I agree with Kerry. Your plumber is probably correct, but the only way to know for sure is to read your documents. The pipe is not a common element because your plumber says so, or because of some logic about sharing the drain pipe. It varies from condo to condo depending on how it was set up in your governing documents.

The association may also say that your AC unit caused the problem, so be prepared for that. Did you change the filters?

The documents don't mention any relationship between common elements and AC drain lines. I'm guessing it's because all the buildings should have been built with separate AC drain lines for each unit. But you know how some contractors are. They are not above cutting corners or neglecting to adhere to the building's blueprints. The plumber has been working with Associations, property managers and homeowners in all kinds of situations involving disagreements about condos and their construction issues for quite a few years.
As far as the filters go, I could have changed them every day but since the AC drain line exits the side of the building and goes right into the ground, I don't think it would have helped.