Tint paints are all water based and will bond perfectly to a fully stable existing water based coating — but the same can't be said for existing oil based paints. Oil based paints were commonly used on doors and trims until fairly recently, meaning they will require a coat of Prep Plus before you can paint over it.
To test what kind of paint you have, get a small amount of methylated spirits* (definitely not turps!) on a rag that is a noticeably different colour to the colour that is currently on the surface. Give it a small rub, if the colour comes onto the rag, you've got a water based paint and if it doesn't do anything beyond cleaning it a bit, it's oil based.
If you have water based paint, all you need to do is give it a light sand and clean before painting. If it's oil based, you need to give it a light sand and use a coat of Prep Plus before painting, otherwise, the paint won't stick properly and you'll find it'll all peel off if you nudge it.
*in a pinch, Vodka or Gin will also work.