Currently, your command setup has a few problems. You've got two different scoreboard scores for the two teams, displaying those scores in different locations, and adding a point to all players (by using just @a without specifying which players you actually want).
The simple solution is to use a team selector in your point-increment system.
/scoreboard players add @a[team=TeamName] PointsName 1
Boom. Your system, as you have it designed right now, will work. This will select all of the players on TeamName and give them a point in their designated scoreboard.
However, from a design standpoint, there's a much better way to do this by using fake players. To start, set up just one scoreboard and put it in the sidebar:
/scoreboard objectives add points dummy Points
/scoreboard objectives setdisplay sidebar points
Now, the /scoreboard players command doesn't actually require you to specify a player that is online. In fact, that player doesn't even need to exist. But it will happily keep a score for them. So, whenever you want to increment the team score, you can just do this:
/scoreboard players add Team points 1
What this will give you is a scoreboard that keeps track of team points in one entry, in one scoreboard. That way, players can compare, at a glance, what the score is, without needing to rely on the tab menu.
Best Answer
To test a fake player's score, use
/scoreboard players testinstead of/testfor.The first
10is the min, the 2nd10is the max.