Team-Arena can be pretty confusing for some players ( especially on the newer servers ).
In order for the server to get the Cross-server Team Arena, a team level must reach/have 120 level.
120-180 is the first bracket of Cross-server Team Arena, meeting the lowest level players.
After that, comes the 180-220 ( Medium bracket, second one ). In order for this to happen, team level must exceed or be 180.
You can avoid doing this by getting low level players in your team and remain in the lower bracket for more wins.
The last bracket I do not remember for sure in TA, I believe it was 231 or 251+ team level.



Cross server :
Being on a new server and trying to enter in a CS can take a bit of time, also leveling faster can help get into a CS.
The brackets for it are : 33-54, 55-80 ( well, now 90+ with the level increase ). They may have changed, however are the ones.
Trying to enter in a CS and being around 55/59 or 60, you'll have atleast a level 70/80+ for sure in it ( also depends on luck ).