Ah that clears things up. Beautiful Greek there: ὡς + ind.perf. -> After [] had ...

So it should've been

"About those things, the local people say [that]: after Sulla himself had written in part 10 of his report/account, K. T. [... insert irrelevant factoid meta-data here...], was sent for him after he [read: Sulla] had won the battle at Chaironeia, bringing word that the T. indicated both a second battle and victory on the [very same] spot within a short time."

Links:
http://www.perseus.tufts.edu/cgi-bin...try%3D%2390046
http://www.perseus.tufts.edu/cgi-bin...try%3D%2317731
http://www.perseus.tufts.edu/cgi-bin...ry%3D%23105574

Note that T. is the (legendary) founder of *the* temple of Delpi, who in turn had a cult & oracle of his own. So T. should be taken to mean the 'oracle of T.', I think.
Finally note the odd " ἧκε " : ind.aor.act.3rd pers.sg. of "hiemi", may also be translated as 'spoke to' i.e. "spoke to him".