I think the standard is that you don't log in unless it's your half of the split. It may be inconvenient in terms of turn pace but it's much less likely to lead to trouble/reloads from people accidentally playing in the wrong order because they don't know if their opponent has or hasn't played yet. If you wait for Civstats to show they've ended their turn that's an unmistakable signal.
$0.02
$0.02
Played: Pitboss 18 - Kublai Khan of Germany Somalia | Pitboss 11 - De Gaulle of Byzantium | Pitboss 8 - Churchill of Portugal | PB7 - Mao of Native America | PBEM29 Greens - Mao of Babylon