Hi I'm trying to work out how to achieve this effect in After Effects / Premiere.
If anyone can shed some light on how to do something similar I'd be most grateful!
Plenty of layers with time offset and different coloring or commercial third-party "feedback" plug-ins that have built-in options to modify the accumulated frames. GenArts Sapphire has one for instance. Really depends. For some scenarios even the stock Echo effect in AE might work, you may just need multiple layers and tweak the settings and then colorize with Colorama or Tritone...
Because these examples have different colors on the repeated images you can't simply use Echo. I would take the first layer animated you want to repeat, duplicate the layer, change the color using what ever method is available to you, then repeat until you get the number of layers you want to repeat. Then reveal the keyframes in the layers by pressing the U key and slide the in and out points of the duplicates around until you get the look you like. It should be pretty easy.
If you are working with footage (a movie) that you want to repeat then you have to isolate the moving element from the background with keying or rotoscoping. I would then apply time remapping to the layer, duplicate it, make the color adjustments, and then adjust the keyframes on the time remapped layers to get the look you want. Also pretty easy.