An initial check up and fecal test is done at the beginning of the quarantine. The reason you wait 30 days and do a SECOND check up is so, if there were any parasites, they will show up in the second test, even if they didn't in the first, given how parasites can take a while to hatch.
During that period is better to keep the cages far away from each other, if at all possible in another room. Gliders can usually sense if there is something different in the house, and so they may start barking, they may not; depends on the glider. The most important thing is that, during this period, you have to make sure that the 2 gliders nor anything they've touched comes into contact. So, you need to clean everything you can between play times (yes, you need to have separate play times), so no diseases are transmitted between them.
After the 30 days, and if the second check up shows everything is ok with the new glider, there should not be concern of transmission, and you can start the introduction process. Below are a few introduction methods:
www.sugarglider.com/gliderpedia/index.asp?Introductions
Hope this helps.