It's crazy that you have to basically buy it, I been trying without totems. I've gotten a 2 slot green and a couple 3 slot demonic but no purple
I used a bunch of totems (I think 20+) and eventually got a purple but it was a 3 slot (was hoping for a 2 slot). It felt great to see the purple spawn (was using a totem) but given the amount of time/totems it took to get there, I couldn't justify doing it all again (granted it's supposedly RNG...but when you are ~20k mares in without a purple...it doesn't feel that way).
Since then whenever I have less than an hour or so to play I go hit a mare spawn to see what I get (no totems) and it's definitely slim pickings. What I haven't figured out is whether the RNG is spawn location specific or whole world (shard) specific (ie any new mare spawned might be colored). I seemed to have more luck hopping around (without a totem) killing 20 mares here and 20 mares there rather than grinding one spot... which seems different than when I was using totems because I'd drop a charge or two and get nothing but shiny/voids or shoguns but the next charge would give me green & demonic. It's been hard to make heads or tails of what to do. I'm also not sure if the calculation is based on anytime a mare spawns or if it's like some sort of a subset qualifier.
That said, there have been people that have posted saying they tamed a purple without a totem so it does seem to happen.
This is a bit off topic but when people pay real $$ for an item to improve chances, I think they (me included) feel a little entitled to eventually getting the thing they are buying said item for. At one point I thought it was a little like SoS where you need to kind of force the ASOS to pop but opening 30 at a time, so I spent 6.5 hours (20 totem charges) straight killing mares without a single purple spawning. Meanwhile I read around that same time about people taming their second and third purple mare and some of those were without a totem. Just doesn't seem like that makes much sense to pay for in game items. That said, I do think the totem will give you more colors in general if you are looking for something like a 2 slot demonic.