Do not let the administrator attempt to trick you.
To get a mark of H from a phylarch tourney - you need to score very large points. Scoring large points is very difficult for low level cities as you need to complete high level agreements to score large - or spend drachma to reset your phylarch energy.
Anyone that has not unlocked the extra action is not working on high level phylarch agreements.
This is a known problem in sparta - and has been brought to the attention of moderators and administrators as well as the old vip agents many many times - they ignore the issue and give false advice instead of addressing the issues.
It is similar to the glory point troubles for new players - they must fight pvp tourneys and score very high points to get these using only light and heavy troops to fight people like myself with troops that have bonuses exponentially higher than the new players - or join a very developed coalition that scores very well in high tier coalition clash events - or get to level 60 to unlock the new emporia.
Admins do not actually play this game. They have no idea what we are talking/complaining about.