First off Vallejo is not a good paint to chip with as it really really reacts to water and therefore it will come off in much larger areas than you want. Second, you have to clear coat over the paint you want to NOT chip, then apply the fluid, then the paint you wish to chip.
The hairspray chipping method works exceptionally well and is far cheaper than chipping fluid. If you want good results chipping use hair spray in two very light coats over the clear coat. Then apply a paint like Tamiya over that and you will have excellent results.
I say this from personal experience with Vallejo paints and chipping. I paint mostly with Vallejo but found I cannot get control over the chipping because Vallejo overreacts to getting wet where Tamiya chips the way one would like.
If you keep using the chipping fluid apply it in light coats only, too much will not work well.
BK
After re-reading you post I can see that your Dark Earth reacted to the chipping fluid. Choose another paint, other than Vallejo or Mig to chip with. You will not have the same reaction. Again, Tamiya paints are awesome to chip with.
On the bench:
Tamiya 1/35 M4A3E8 "Fury" with crew,
1/32 Kittyhawk Kingfisher,
1/35 Meng Panther Ausf A Early,
1/48 Pro Modeller P-51C "Boise Bee"
On Deck:
Tamiya 1/48 F4U Birdcage,
1/25 Revell 32 Ford Coupe
1/12 Bandai "Mandolorian"
2022 Completed:
1/25 Revell 29 Highboy
1/48 Tamiya Sea Harrier
1/25 Revell 70 Boss 429 Mustang