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Strange occurrence in the battle tree

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Hello all. Had a really strange occurrence at the battle tree today, and I’m wondering if anyone has an explanation for this. I was playing super doubles at the battle tree in ultra sun, and I faced blue. I led with Tapu koko (Timid nature, 252 speed EVs, speed IV of 31, holding a life orb) and kartana (holding fightinium Z). Blue led with aerodactyl and tyranitar. On turn 1, I used detect with kartana and protect with tapu koko. His aerodactyl mega evolved and used fire fang on kartana, then he did dragon dance with his tyranitar. On turn two, I switched kartana out and replaced him with charizard, and I used thunderbolt from tapu koko on aerodactyl, narrowly missing a KO. Blue then did another dragon dance with tyranitar, and finally used fire fang from aerodactyl on charizard, not making much of an impact. On turn three, I mega evolved charizard into mega charizard Y, and attempted to go for volt switch on his aerodactyl from tapu koko, but tyranitar moved first, knocking tapu koko out with earthquake. Luckily I still won the match by the skin of my teeth (I have been trying to get that damned stamp for ages, more often than not losing to some BS like bright powder or two freezes in a row), but how could this occur? Maybe I’m just being dumb but surely tapu koko should move first, because he is max speed and base 130, while tyranitar is base 61, so even if he is max speed surely he underspeeds Koko when that is doubled to base 122. I’ve been searching all over for how this could happen, and have found nothing. The only possibility I can think of is a speed boosting item on the tyranitar, but I looked up blue’s sets and the item can only have been a chople berry. Again, maybe I’m just being a fool but can someone explain this to me? Sorry for the long post.
 
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You wouldn't calculate from Tyranitar's Base, check out Serebii's stats and it is pretty clear. At Lv 50 (which, they are set to in Battle tree, yes?) Tapu Koko's Speed (as you explained), would be an even 200 (394 at Lv 100). If Tyranitar has Max Speed, Jolly Nature, and 31 Speed EVs, then his Speed at Lv 50 would be 124 (243 at Lv 100). Doubled after the two Dragon Dances, Tyranitar would be the faster, at 248 (486 at Lv. 100). If that is how everything calculated, he would be faster than you.

For reference, his Speed after one Dragon Dance would be 186, below Tapu Koko's 200.

Also, technically, Tyranitar wouldn't even need a boosting Nature to outspeed you. With a neutral Nature (most likely Adamant), his doubled Speed at Lv 50 would be 226. With a hindering Nature, which is highly unlikely, his doubled Speed at Lv 50 would be 201, still just enough to outrun Tapu Koko's 200. Obviously, this is assuming that he has 31 Spd IVs and 252 EVs, but when you look at the math, it is actually rather unlikely that Tapu Koko be the faster Pokémon in this circumstance.

For the reference that I am looking at, check out Tyranitar #248 - Serebii.net Pokédex (For Tyranitar's Stats) and Tapu Koko #785 - Serebii.net Pokédex (Tapu Koko's Stats).

That is how I understand it anyway, someone please correct me if I am wrong.
 
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Thank you very much for your thorough explanation, you are completely correct as far as I can see. I had assumed that it was a linear relationship between a given pokemon's base and maximum stats, so I could calculate from base stats and the same result would apply as when calculated using max stats. Evidently, this is not the case - the differential between minimum and max speeds is not even the same between the two pokemon, which I've always foolishly assumed would be the case for any two pokemon! Thank you again, I shall have to be far more careful when I look at base stats in the future
 
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