Do we have to have Cyborg DataChannel active when we claim our shipments to get a bonus or is it enough for it to be active during daily arrival?
Example:
Our shipment arrives at 1pm and Cyborg DataChannel expires at 2 pm. 2 people claim their shipments (1st at 1:30pm, 2nd at 2:30 pm). Will both of them get shipment with bonus or just the 1st one?

I believe you will get it after it expires. Because it says (1) Daily shipment of Legion Base resources ready: xxxxx Research Points, xxxxxArtifact Points Total. (Divided Evenly Between all Eligible Members)
If thats the amount before with the data channel on it will give the same as someone that claimed with it on.

The buff must be up when the shipment becomes available. It does not count if applied after.

so it doesn't matter if it's activated when I claim the shipment as long as it was active during daily arrival?
I'm asking as we had it active during arrival today but it expired few minutes after that and we only got 38k each when normally it's 44k+ (but we claimed when CDC expired). I heard from few ppl that CDC must be active for both arrival and claim. So I'm still confused. i think we'll have to test it by having someone claiming with CDC on and someone with CDC off.

No it only has to be active when the shipment arrives, when you claim it matters not.