Aluminium usually welds okay without too much distortion, Stainless is one of the worst.
I woudn't worry about a jig, just check it for true after you have finished. It will be hard to build a jig to hold everything & allow access to weld everywhere too.
Aluminium needs to be hot to get decent penetration, & the heat will travel throughout the whole arm so welding it bit by bit isn't an option. Once you get it hot to weld you need to keep going till it's finished to get decent welds.
The fact that your welder thinks he can weld it bit by bit makes me think he hasn't got much experiance at welding aluminium or that he intends to use a MIG.
Some swingarms get chew marks from the chain, these are usually small & you can get in quick to fill these without detroying the heat treatment too much but to weld a gusset up the length of the arms will effect the heat treatment of the alloy.
You may get away without heat treating but I can tell you it will be weaker than it could be so if you want any peace of mind while riding it I would get it heat treated back to T6.
The tubing in my swingarms I have annealed to T0 in order to bend the banana shape into them. By the time I have finished welding them completely the whole swingarm is as soft as butter. Once welding is finished I check them for true, clamp a spacer inbetween the axle pivots & send them off to brought back up to T6.
Check your local trades guides for heat treatment companies, it's no big deal to get things done properly.