That is why any quote/contract needs to be put in writing. Really depends whether the OP thinks it is worth fighting, for what is a pretty minimal sum.
When did $250 become a minimal sum... that's a lot of money for most people out there. There's no way I could cough up $250 out of the blue.
If I arranged for something like this to be done I would have to budget for it. I would get a quote from a couple of different installers and then when a total was agreed on I would put the money aside.
I'd be asking him to remove the new aerial and put the old one back but that's just me. Actually I would have put the splitter and cable in myself :-)