I don’t know what product you were using so I can’t unfortunately comment on the instructions.
Your cuticles should never be completely removed. Sometimes the names of products on packaging are misleading, especially when they’re called "Cuticle Removers". You need your cuticles to protect your nail bed from bacterial and fungal infections. What most products do, though, is soften your cuticles so you can push them back. However, if you find there’s excessive cuticle skin after you’ve pushed them back, you should see a professional manicurist who will gently and very carefully remove the excess portion with a manicure scissors. This is very sensitive skin, so I don’t recommend you clip or cut anything yourself at home.