Doubleheader situation

[canadaump6]

In game 1 of a doubleheader, base umpire ejects a player for a personal remark. The rest of the game is completed without any other problems. The teams need to start the second game of the doubleheader asap because the lights are on a timer.

How much time is reasonable to give the umpires between games? Is it acceptable that they spend some of that time phoning the league president asking if the ejected player is suspended for the second game of the doubleheader, or should whatever suspension happens take place in a game after the doubleheader when the umpire has filled out an ejection report?

I'm asking this because as a player I had a doubleheader where a player on my team was ejected, and the umpires took over 20 minutes in between games, which I suspect was because they were phoning the guy in charge of the league to ask if the ejected player gets a suspension. They were leaving phone messages and calling different numbers to get in contact with him, so it took longer than just a quick phone call. Given the situation of needing to get the second game in as soon as possible, was it reasonable that they would take extra time phoning the convenor rather than filling out an ejection report after the doubleheader and letting the convenor decide further consequences?