Apologies for the late response, sirs.
I've always been under the impression that what you called a pump was not a real pump, Titio. What you call a sexy pump always been a pump and so you'll find oldschool players not making a distinction between the two (like Shady).
I think it was quite obvious that Shady meant a sexy pump when he called for a pump, as you could see in his moves. I wasn't even aware that the oldschool pump had been downgraded to what titio did here, though I'm not an active warmer player.
At any rate, warmers are about the challenge of performing tricks, not about making things easier for yourself, so in my opinion, pump should be sexy pump. If you and your opponent agree before the game that pump and sexy pump are different things and are both allowed, I'm fine with that, but if there's no mention, then pump = sexy pump.
I'd also like to note that Shady's first H wouldn't count, since Titio didn't call his moves before he did them.
Normally, quitting the game would be considered a forfeit, but considering this issue was clearly messing up the dynamic of the game, I can understand why it happened. However, for future games where something like this happens: please finish the game. If you get to HORSE, but (for example) two of them were because of misunderstandings, then that game will be voided and will be continued with you being at HOR. The next person to quit in order to ask what is supposed to be done will forfeit their game, regardless of whether they were right or not.
All this would put Shady at an advantage, but considering this game was such a mess, I think it's best forgotten. So my call would be to replay the game entirely.