I don’t know what ASI stands for, but is this a commercial sub-contract?
If so I would expect the designer to assume tube material made to size, though whether you (or I ) can obtain 7mm o.d. X 1mm wall, cold-drawn, m.s. tube easily is another matter. It seems an unusual diameter. Perhaps he knows a supplier!
I would also expect the +/-0.005″ tolerance to be on thickness and concentricity throughout the length, which as we’ve seen so far won’t be impossible, but not easy to achieve.
Re using the slot for a drive-dog: I’d say no.
I’d cut the slot after turning the outside, and a 3mm slitting-saw might give better results than a slot-drill.
Maintaining concentricity and finish on a long, plain tube is enough of a headache as it is, and you don’t want the added complication of a widely interrupted turning cut along a thin-walled tube. It could too easily catch and wreck the workpiece at least, and even if it does not do that it may create peculiar edge effects along the slot.
Do it afterwards, holding the tube in a channel or Vee-groove for its full length, but be aware either the clamping might close the tube onto the cutter or the tube will spring open slightly, putting it over-size.
…..
Apart from which:
I’m not sure this forum is appropriate for advice for commercial work though. Anyway if for regular military manufacturing, that is normally tied down to all sorts of accreditation and QA schemes.