If you are printing with Solvent inks You Must give at least 24 hours to off gas and normalize.
Even if you are cutting just outside the printing area.
My Previous printers were Seiko CP, HP9000, L265 & L560.
What you are describing sounds like an adhesion Issue.
If you are applying decals to Plastics or Glass you need vinyl with LSE Adhesive
Low Surface Energy. 3m 3650, IJ 180 C LSE and Low Cost 3m IJ39.
The 39 has vastly improved.
Outside of 3m you have Convex and it aint cheap!
I do not purchase Oracal, Avery, or Calon products due to the bulk nature of my
products or anything fiberglass.
Also important is if you laminate your media 24 hours after off gassing, I like to give
another 24 hours for everything to normalize.