Okay, pushing 2 electrocutes in P1 is what we usually do when doing 10-man with alts. Having the Ony tank also tank the adds is a bit meh. Rather have someone else kite them and have them die in a nice pile on the side. Stunning adds is a bit risky. You need to keep a close eye on the timer for shadow flame or else they'll be stunned inside a fire and won't go down.
That ought to take care of the mana problem somewhat. Who is healing what? Paladin, shamy, druid... Are you healing the Ony tank all by yourself? That's silly. Get help with tank healing
Have Mana Tide in P1 already. Somewhere between the first and second electrocute perhaps. There's a lot of time to reach the pillars, a lot of time to allow HoTs to tick and bring people back to full hp. Mana Tide should then be saved for P3 when everybody is in reach of it again. The shamy should not use it on his pillar. It's a waste. He needs to manage his mana.
I think that in our 10-mans, we did it similar to 25-man... Preferred healers for the kiter tank are healers with decent CDs. Paladin, priest preferably, though the other day, I (shamy) helped with the kite tank as well, but we didn't have an ideal setup anyway, so someone had to. Anyway... Maybe you'd like to have the paladin heal the kiter, the shamy on Nef's tank and you'd take care of the electrocutes and HoT the Nef tank. The shamy can put down a healing rain too if his mana allows. There really is so much time between the crackles that HoT's will do the job on their own. Also make sure that the shamy's healing stream totem affects all the people in his group. It won't do much for the kiters as the range just isn't enough. So have the shamy in a group that huddles in the middle, with the Nef tank in his group as well. The totem ticks for around 1.7 - 2k the lower someone drops. It helps. It also helps with resisting a bit of the crackle dmg if glyphed (every resto shamy should have it glyphed).
Remember that after everybody is brought to full hp after the 20% electrocute, you will no longer need to heal the raid. They'll still get the 10% electrocute, but as nobody except for the tanks should be getting any damage from that point on, they can sit there happily with 10% hp. So after having thrown HoTs on everyone at 20% to enable them to survive the 10% AoE, you should see if the kiter tank healer needs some help. I know most of our wipes happened at <20% hp because the adds became hard to handle and kiter tank and healer were out of cooldowns or something. So that's something to keep an eye on.
I hope some of my rambles are helpful. As there are no logs, it's hard to tell what exactly is going wrong aside from your mana bar being bone dry.