Nine times out of ten it's not the colour, mate — it's the sheen. A fresh dab of paint sits at a slightly different gloss level to the wall around it, which has cured and picked up a few months of light scuffing and dust. Catch it at a raking angle and you'll see a patch even when the colours are identical.
Three things cause flashing:
Sheen difference. Even matt emulsions have a touch of sheen, and a wet brushload looks different to fully cured paint. Higher-sheen finishes — anything in eggshell or satin like Little Greene Intelligent Eggshell or Dulux Diamond Matt — flash far worse than a true dead-flat. This is exactly why Farrow & Ball's properly chalky finishes (think Estate Emulsion in Pointing or Cornforth White) are more forgiving for spot repairs.
Thickness and build-up. A thick dab leaves a raised edge that catches light. Touch-ups want to be thin and feathered, not loaded on.
Different batch or applicator. A roller leaves fine stipple texture; a brush leaves none. Touch up a rollered wall with a brush and the texture alone gives it away — even with the exact same tin.
For the repair: use the same tin (not a fresh one), thin it slightly, and apply with the same tool the wall was done with — a small mini-roller for rollered walls. Feather the edges out so there's no hard line. Do it in daylight, not under a lamp.
If it still shows, you've two options. On a flat, chalky finish you can usually get away with a feathered patch. On anything with sheen, or a wall that's seen a few years, stop fighting it — paint the whole wall, corner to corner. Natural breaks (corners, door frames) hide the join; a patch in the middle of a wall never will. Keep your offcut tins labelled and stored cool, and they'll serve you for years.