Yeah, the Chitauri invasion is a little too recent for that to really work. Jessica's backstory is that her superheroing days are a good 10 years prior--give or take--to when her story starts.
As for tying it into the same chemical spill that got Matt...there's a few problems with that idea. Firstly, Matt and Jessica have *vastly* different powers and abilities (Jessica can fly, is physically very strong and tough, though not invulnerable), so unless that stuff was the product of someone trying to synthesise terrigen crystals (a possibility, for sure) such vastly different outcomes seems unlikely.
Second, in the comics Jessica spent some time in her youth (late teens, early 20's ish) as an active (though second stringer/wannabe) superhero, which in the MCU almost certainly means she was indexed and probably working for SHIELD. If they knew that crash had produced one superhero, you'd think they'd have checked out the other kid (Matt) known to have been hit by that stuff. On the other hand maybe they did and he's on the index, but has since fallen through the cracks after the fall of SHIELD. That or Stick managed to hide him from SHIELD somehow.
Aside from that, I'm not sure if it was ever specified that the chemicals are what gave Matt his abilities or just the fact of being blinded activated a latent (Inhuman?) ability that was already there but dormant.
Now tying Jessica's & Cage's origins back to the same source makes a bit more sense since their powers are more in line with each other and could both be the result of someone else (Oscorp sponsored by Hydra if we really want to tie the NY stuff together) monkeying around with Erskine's formula again.
