Praise be to Allah.
May Allah reward you for your keenness to understand the matters of your religion, especially the prayer. We ask Allah to help you to fulfil this great trust, the trust of leading the people in their prayer.
With regard to your question, it covers a number of topics:
1 – What was narrated in Saheeh Muslim is: the Sahaabah sought permission to fight those leaders who changed and altered things to the extent that they introduced new things that the Sahaabah would denounce them for. Undoubtedly delaying the prayer from its time is one of these changes, but they were not given permission to fight them so long as the leader still established regular prayer.
It was also narrated in Saheeh Muslim that the Prophet (peace and blessings of Allah be upon him) said that there would be leaders who would delay the prayer from its time, so he told the Sahaabah to pray the prayer at the proper time, and to make their prayer with those leaders naafil. There follow some of the ahaadeeth:
(i)The ahaadeeth which indicate that it is not allowed to fight the leaders who change and alter things, so long as they do not give up prayer altogether:
It was narrated from Umm Salamah that the Messenger of Allah (peace and blessings of Allah be upon him) said: “There will be rulers whose good deeds you will like and whose bad deeds you will dislike. One who sees through their bad deeds (and tries to prevent their repetition by his hand or through his speech), is absolved from blame, but one who hates their bad deeds (in the heart of his heart, being unable to prevent their recurrence by his hand or his tongue), is (also) safe (so far as Allah’s wrath is concerned). But one who approves of their bad deeds and imitates them is spiritually ruined.” They asked. “Shouldn't we fight against them?” He replied: “No, as long as they still pray.” (Saheeh Muslim, no. 1854)
It was narrated from ‘Awf ibn Maalik that the Messenger of Allah (peace and blessings of Allah be upon him) said: “The best of your leaders are those whom you love and who love you, who pray for you and you for them. The worst of your leaders are those whom you hate and they hate you, whom you curse and they curse you.” He was asked, “O Messenger of Allah, should we not fight them by the sword?” He said, “No, not so long as they establish the prayer among you. If you see anything on the part of your leaders that you dislike, denounce that action but do not break your allegiance to them.”
(ii)The ahaadeeth which indicate that the leaders would delay the prayer from its time, but the Prophet (peace and blessings of Allah be upon him) still enjoined praying with them and he did not enjoin fighting them:
It was narrated that Abu Dharr said: “The Messenger of Allah said to me: ‘What would you do if you had leaders who delayed the prayer from its proper time or killed the prayer from its proper time?’ I said, ‘What do you command me to do?’ He said, ‘Pray the prayer at the proper time, then if you join them pray with them, and it will be a naafil prayer for you.’”
2 – What is meant by ‘leaders’ (lit. imams) in this hadith is rulers, as is clearly stated in the hadiths of Umm Salamah and Abu Dharr (may Allah be pleased with them).
3 – This is the focal point of the question: what is meant by delaying prayer from its proper time is delaying it from the preferred time. Imaam al-Nawawi (may Allah have mercy on him) said in his commentary on Saheeh Muslim:
“The Prophet (peace and blessings of Allah be upon him) said: ‘What would you do if you had leaders who delayed the prayer from its proper time or killed the prayer from its proper time?’ I said, ‘What do you command me to do?’ He said, ‘Pray the prayer at the proper time, then if you join them pray with them, and it will be a naafil prayer for you.’ According to another report he said, ‘Pray the prayer at the proper time and make your prayer with him naafil.’ What is meant by ‘killing’ the prayer is delaying it, and making it like a dead person whose soul has departed. What is meant by delaying it from its proper time is delaying it from the preferred or best time, not delaying it from its time altogether, because what was narrated from the earlier and later rulers is that they delayed it from its preferred time; none of them delayed it from its time altogether. So we must interpret these reports according to what actually happened.”
(Sharh Saheeh Muslim, 5/47 ff)
Thus it will be clear to you that there is a difference between establishing prayer and delaying it. The ahaadeeth are not referring to delaying the prayer from its time altogether until the time for the prayer is over and then praying, rather what is meant is delaying it from the preferred time, such as delaying ‘Asr until the sun has turned yellow, or delaying Maghrib until the red afterglow has almost disappeared, and so on. What is meant by not establishing prayer is not doing it at all. Thus we may reconcile between the ahaadeeth. And Allah is the Source of strength.