There is no right or wrong answer for your question, 2v2 and 3v3 are differant and if you do "serious" arenas you will want to swap reforges and maybe gems every times you do 2s or 3s.
In 2s you can fight 3 kinds of teams,
You and your partner vs Healer/DPS Team,
You and your partner vs DPS/DPS Team,
You and your partner vs Healer/Healer Team.
I will only talk about the two firsts.
Usually in Healer/DPS teams, the pressure going out without any CDs poped is quite low, so going for spirit would be the best choice here and mastery the second best as it is more efficient than crit or haste. Depending on who you play with, you may be able to get resets, meaning you have 10-15 seconds out of combat while whoever you play with peels for you, so if you chose to go with Crit and mastery instead of Spirit and mastery you will be able to drink every now and then to restore mana. However, if you know that your partner is not so great i wouldnt recommend this. Usually paladins dont run oom if they play right against 1 dps and 1 healer.
Against DPS/DPS games wont last very long, so Crit/Mastery is more efficient as it will reduce the pressure, the only downside is it gives your partner a tight time limit to beat up the other team, depending on his gears it may not be a great idea.
So, to conclude for 2s, the way you want to reforge should be based on how Good/Geared your partner is.
In 3v3 things can be hard to deal with, games can be long and intense, and every healers get in a "OOM" situation at some point. If you play a comp like "TSG" or "Kitty CLeave" that simply runs in and try to get a kill on that poor resto shaman, go for Mastery and Crit, screw spirit, games wont last long enough for it to be useful. If you play a control comp, you will usually have reset opportunities, but I would suggest that you take mastery and crit over most and burst from other teams are scary and those lucky crits are life savers.
So for 3s I recommend that you take as much mastery as you can, along with as much crit as you can get. I played kitty cleave last season and I would reforge all my spirit into crit/mastery to have the best healing output possible.
For the gemming, I dont like to gem for Mastery or int or crit, I go with resiliance. Many people say Hpallies are impossible to kill, thats because they dont play one. They sure are resiliant, but mages that get a good CS on you will kill you if you dont have trinket or bubble available for their following DF. Paladins ARE good swap targets if they are in the wrong position, or even if they are in the right position. Being trained all game long is usually fine but hardswap on the paladin when both your partners are CCed will force a CD.
In RBG take Mastery and spirit to stay in the fight as long as possible.
Gems should be Intellect + PvP Power/Resilience i tend to lean more towards Resilience in most of my slots but i dont have the math on it.
The list on Noxxic is pretty complete.
he only differences in my set and theirs is that im using Enchant Boots - Greater Haste instead of the Enchant Boots - Pandaren Step but that is personal preference.
And by tinker are u talking about your talent tree? Im confused of what exactly you are looking for.