Charged Conference???

[VaCoach]

I saw this last night and wanted to know how was correct. Third base coach called time to talk with batter, immediately the coach of the other team ran out to the mound to talk to his pitcher. As the third base coach stopped his offensive conference, so did the pitcher's coach. Umpire told defensive coach that was one of his 3 charged conferences, he disagreed and said he had right to talk when the third base coach called time. Who is correct? I have seen third base coach talk to a batter while a defensive conference was going on at the mound. Is this the same thing??