I don't think it's his choice of healing, but more choice of gemming/glyphing.
His spell usage is fine, little more HST could be used, maybe a little less rain since I doubt it's as useful on 10 man as it is on 25. Keeping rain up full time is great, but you can't really complain you're going oom if you are
When is he dropping mana tide? When he's at 70% mana or when he realises he's oom? Potions of focus are 45k mana and 10 seconds of mana regen on top!
He has riptide glyphed, it's a huge mana drain, and not nearly as effective without the initial heal. He should be using it on CD without the glyph, and I guarantee his riptide numbers won't change much and his mana will go a long way. He can replace this with glyph of TC or TR, whichever he prefers as these provide some positive mana return. I'd personally choose TC.
He's using primal elementalist but I can't see him activating the buff from either elemental? 10% healing increase, 10% less healing to do, saves mana!
In terms of gearing, more spirit! He's using a few pure int gems, these can be changed for 80int/160 spirit, every little helps! If he's got the gold, drop the Courtesan Figurine and get a DMC. The regen from this is insane. Also chest enchant to spirit and weapon enchant to jade spirit.
Also from the logs, he didn't have a flask? That's 1000 spirit right there!
TL
R. healing is fine, can make his mana stretch further!