I still paint with enamels for the most part, and acylics only for the metal colours and bases ('cos they dry quicker). Therefore, to get off the paint and white spirit from brushes when using any of these paints, some form of soap is needed, even for acrylic residues. I have a post of old bits of soap topped up with water, though liquid soap straight from its dispenser could be used.
Actually, being the tightwad that I am, I’ve always kept and used those old small salmon and fish-paste jars. If you keep the lids you can get the right consistency and colour then re-seal them for later use.
(You have to give ‘em a good clean-out first, or the smell from your figures makes you ravenously hungry... ...which is another good way of ensuring that games end quickly...but does attract the cat. )