Hello,
Regarding skipping QT, I highly advise against this. Zebrasoma tangs such as yellows, gems, purples, sailfin, black, etc can be VERY resilient to parasites. If the person did not stringently quarantine, there is a high liklihood that it will bring parasites to your system which will infect everyone. Powder Blue tangs are among the most susceptible and I've not seen many successes with them more than a few months in the absence of proper QT.
Regarding adding them - I would add them together. This increases your chances. Gem can be fiesty, but adding multiples at a time will spread the aggression well. In a large tank with few other fish, the Gem will be accustomed to not needing to share its' space with many direct competitors. This is why it's heckling the foxface a bit. The risk factor in lowly stocked tanks is higher for this reason. Thankfully, Zebrasoma tangs don't seem to "hold grudges" against new additions as long or violently as their acanthurus cousins (particularly powder blue, achilles, powder brown, goldrim, clown tang, and sohal tang - in no particular order). Thus, if the new fish can survive the first couple of days without getting too beat up, things will likely be fine. I would be surprised if the gem would harass a coris wrasse, so I wouldn't worry about that. The coris can hide in the sand to stay safe if things get ugly (and likely will either way when added).
One option is a large acclimation box for adding new fish. This is best used when adding one tang to a tank containing a tang or tangs. Even better would be to add several at a time as mentioned. Adding mirrors on either side of the tank to distract the aggressor can also help.
Though a yellow tang and gem are of the same genus, and thus a bit at risk of clashing harder than the others -- I find that oftentimes zebrasoma co-exist better within their genus than many others. Of course, individual fish have indivudual personalities and thus there are NO guarantees.
Good luck!