Weird Situation

[SMEngmann]

Today I was playing in a semi-pro baseball game and I was hitting with a count of 2-2. The pitcher was taking a long time checking the runner and going over the signs and I requested time right before he began his motion. The plate umpire started to verbally grant timeout saying "Ti....." and then the pitcher began his motion to the plate and the umpire didn't complete the word "time." I started to back out when I heard the umpire apparantly granting time and the pitcher finished his pitch, and the plate umpire then rang me up. I argued saying that I had been granted time as soon as the umpire began to grant me time, and that I wasn't in position to hit. The umpire told me, "I started to grant you time, but never finished." Eventually the umpires conferred and agreed that time had been granted and I got to finish my AB. My question, as a player, coach and a fellow sports official, is: At what point is timeout considered granted by an umpire and also, did the umpires handle the situation properly? Could this have been a situation where, when I was allowed to continue hitting that a protest could have been lodged by the other team? I ended up my AB with a groundout advancing both runners, but I'm more curious than anything. Thank you.