New pet tames can drop, sadly the information available is pserver based. Hopefully they will release it soon. I finally managed to start getting Nine Tail tames as of last night, after about 15 HE Gums I got 7 tames. It took 5 to get the pet itself, so assume other new pets to be about that 5 ~ 10% chance to tame. Just remember we don't have the new pet foods yet so that is defo a nono.
Also, it will take you longer to loyal your pet up if you rely on autofeed. Autofeed procs exactly as the pet turns "hungry". When feeding at that stage, it actually gives the least amount of loyalty points possible. Not only that, but if you feed it at the optimal time of it just hitting "neutral", not only does it get the most points, but it also is 4x faster period, as it takes 4 of these optimal feeding times to hit "hungry". Only use autofeed if you login daily and afk or as a general farming method, use that pet hunger bar otherwise if you wanna really make it quicker.
You must be the person I asked to show me the tame yesterday, on the Enchanted Peach Tree map? If so, thanks for giving me hope! I would have given up by now if I hadn't seen that you actually got those + the egg... I have like 250 dead branches, several OBBs and even the card!! But no tames.