Flame surge + Arcanist brand in Explosive Arrow build question

Been messing around with the build this league, mostly following Zizaran build. I see he has Flame surge linked to Arcanist Brand, but Flame Surge is left at level 1. Flame surge main function is to create burning ground, thus increasing your ignite damage. I presume the hit from FS won't do any damage because of Ancestral Bond, but why not level it up for a bigger AoE?

My understanding of the mechanics of Arcanist Brand is that you only pay mana (or health with lifetap) on Arcanist Brand and it doesn't appear to have any scaling. So it wouldn't cost any more if Flame Surge was level 20 and created a bigger ae, right?

you gotta pay the mana cost of a skill, when it is triggered unless specified otherwise (Mjölner) and the damage scaling is not very high, when you lvl it up, because the burning ground dot will not be improved.

to be honest i have no idea, if gem lvl's will increase the burning ground aoe